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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

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Gennadiĭ Mikhaĭlovich Goluzin and geometric function theory
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by G. V. Kuz′mina
Translated by: N. Yu. Netsvetaev
St. Petersburg Math. J. 18 (2007), 347-372
DOI: https://doi.org/10.1090/S1061-0022-07-00954-5
Published electronically: April 10, 2007

Abstract:

G. M. Goluzin crucially influenced the development and extension of geometric function theory. His results received world-wide recognition, and his monograph “Geometric theory of functions of a complex variable” has been a reference book for several generations of analysts.

This paper is a survey of Goluzin’s scientific work on the occasion of the 100th anniversary of his birth.

References
  • On some estimates for the functions realizing univalent conformal mapping of the disk, Mat. Sb. 36 (1929), no. 1–2, 152–172. (Russian)
  • An extension of the Carleman formula and its application to the analytic continuation of functions (jointly with V. I. Krylov), Mat. Sb. 40 (1933), no. 2, 144–149. (Russian)
  • Solution of basic plane problems of mathematical physics for the case of the Laplace equation and multiply connected domains, bounded by the circles (method of functional equations), Mat. Sb. 41 (1934), no. 2, 246–276. (Russian)
  • Solution of the space Dirichlet problem for the Laplace equation and the domains bounded by a finite number of spheres, Mat. Sb. 41 (1934), no. 2, 277–283. (Russian)
  • On the theory of univalent conformal mappings, Mat. Sb. 42 (1935), no. 2, 169–190. (Russian)
  • Solution of the plane heat conductivity problem for multiply connected domains, bounded by circles, in the case of the presence of an isolating layer, Mat. Sb. 42 (1935), no. 2, 191–198. (Russian)
  • On the majoration principle in function theory, Mat. Sb. 42 (1935), no. 6, 647–650. (Russian)
  • On distortion theorems in the theory of conformal mappings, Mat. Sb. (N.S.) 1 (43) (1936), no. 1, 127–135. (Russian)
  • Sur la représentation conforme, Mat. Sb. (N.S.) 1 (43) (1936), no. 3, 273–282. (French)
  • Sur les théorèmes de rotation dans la théorie des fonctions univalentes, Mat. Sb. (N.S) 1 (43) (1936), no. 3, 293–296. (French)
  • On distortion theorems for the conformal mapping of multiply connected domains, Mat. Sb. (N.S.) 2 (44) (1937), no. 1, 37–64. (Russian)
  • Some covering theorems for the functions regular in the disk, Mat. Sb. (N.S.) 2 (44) (1937), no. 3, 617–619. (Russian)
  • An addendum to the work “On distortion theorems in the theory of conformal mappings”, Mat. Sb. (N.S.) 2 (44) (1937), no. 4, 685–688. (Russian)
  • On conformal mapping of two connected domains, bounded by rectilinear and circle polygons, Conformal Mapping of Simply Connected and Multiply Connected Domains, “ONTI”, Moscow–Leningrad, 1937, pp. 90–97. (Russian)
  • Conformal mapping of multiply connected domains on the plane with slits by the method of functional equations, Conformal Mapping of Simply Connected and Multiply Connected Domains, “ONTI”, Moscow–Leningrad, 1937, pp. 98–110. (Russian)
  • Some coefficient estimates of univalent functions, Mat. Sb. (N.S.) 3 (45) (1938), no. 2, 321–330. (Russian)
  • On the method of continuity in the theory of conformal mappings of multiply connected domains, Mat. Sb. (N.S.) 4 (46) (1938), no. 1, 3–8. (Russian)
  • G. M. Golusin, Iterationsprozesse für konforme Abbildungen mehrfachzusammenhängender Bereiche, Rec. Math. [Mat. Sbornik] N.S. 6(48) (1939), 377–382 (German). MR 0001846
  • G. M. Golusin, On limiting values of Cauchy integral, Leningrad State Univ. Annals [Uchenye Zapiski] Math. Ser. 6 (1939), 43–47 (Russian). MR 0003212
  • G. M. Golusin, On complete systems of functions in the complex domain, Leningrad State Univ. Annals [Uchenye Zapiski] Math. Ser. 6 (1939), 48–51 (Russian). MR 0003245
  • G. M. Golusin, Zur Theorie der schlichten Funktionen, Rec. Math. [Mat. Sbornik] N.S. 6(48) (1939), 383–388 (Russian, with German summary). MR 0001857
  • G. M. Golusin, Interior problems of the theory of univalent functions, Uspekhi Matem. Nauk 6 (1939), 26–89. MR 0000290
  • G. M. Golusin, Über $p$-valente Funktionen, Rec. Math. [Mat. Sbornik] N.S. 8 (50) (1940), 277–284 (Russian, with German summary). MR 0003234
  • G. M. Golusin, Über Koeffizienten der schlichten Funktionen, Rec. Math. [Mat. Sbornik] N.S. 12(54) (1943), 40–47 (Russian, with German summary). MR 0009052
  • G. M. Golusin, Zur Theorie der schlichten Funktionen, Rec. Math. [Mat. Sbornik] N.S. 12(54) (1943), 48–55 (Russian, with German summary). MR 0009053
  • On the wing theory in plane-parallel flow of fluids, Mat. Sb. (N.S.) 12 (54) (1943), no. 1, 146–151. (Russian)
  • G. M. Golusin, Some estimations of derivatives of bounded functions, Rec. Math. [Mat. Sbornik] N.S. 16(58) (1945), 295–306 (Russian, with English summary). MR 0013802
  • G. Golousin, On the theory of univalent functions, Rec. Math. [Mat. Sbornik] N.S. 18(60) (1946), 167–179 (Russian, with English summary). MR 0016132
  • G. Golusin, On the problem of Carathéodory-Fejér and similar problems, Rec. Math. [Mat. Sbornik] N.S. 18(60) (1946), 213–226 (Russian, with English summary). MR 0016478
  • G. Golusin, On some properties of polynomials, Rec. Math. [Mat. Sbornik] N.S. 18(60) (1946), 227–236 (Russian, with English summary). MR 0016477
  • G. M. Golusin, On the distortion theorems for “schlicht” conform representation, Rec. Math. [Mat. Sbornik] N.S. 18(60) (1946), 379–390 (Russian, with English summary). MR 0020634
  • G. M. Golusin, On the number of finite asymptotique values of integral functions of finite order, Rec. Math. [Mat. Sbornik] N.S. 18(60) (1946), 391–396 (Russian, with English summary). MR 0016479
  • G. Golusin, On distortion theorems and coefficients of univalent functions, Rec. Math. [Mat. Sbornik] N.S. 19(61) (1946), 183–202 (Russian, with English summary). MR 0018753
  • G. Golusin, Method of variations in the theory of conform representation, Rec. Math. [Mat. Sbornik] N.S. 19(61) (1946), 203–236 (Russian, with English summary). MR 0018752
  • G. Golusin, Estimates for analytic functions with bounded mean of the modulus, Trav. Inst. Math. Stekloff 18 (1946), 87 (Russian, with English summary). MR 0020633
  • The variational method in conformal mapping, Nauchn. Bull. Leningrad. Gos. Univ. no. 9 (1946), 3–5. (Russian)
  • G. Golusin, Method of variations in the theory of conform representation. II, Rec. Math. [Mat. Sbornik] N.S. 21(63) (1947), 83–117 (Russian, with English summary). MR 0023908
  • G. Golusin, Method of variations in the theory of conform representation. III, Rec. Math. [Mat. Sbornik] N.S. 21(63) (1947), 119–132 (Russian, with English summary). MR 0023909
  • G. M. Goluzin, Some covering theorems in the theory of analytic functions, Mat. Sbornik N.S. 22(64) (1948), 353–372 (Russian). MR 0027054
  • G. M. Goluzin, On the coefficients of univalent functions, Mat. Sbornik N.S. 22(64) (1948), 373–380 (Russian). MR 0026688
  • G. M. Goluzin, On distortion theorems and the coefficients of univalent functions, Mat. Sbornik N.S. 23(65) (1948), 353–360 (Russian). MR 0029431
  • On analytic functions with the bounded mean modulus, Uchen. Zap. Leningrad. Gos. Univ. no. 111 (1949), 120–125. (Russian)
  • Variation deduction of distortion theorems for univalent functions, Uchen. Zap. Leningrad. Gos. Univ. no. 111 (1949), 126–134. (Russian)
  • G. M. Goluzin, Some inequalities for analytic functions, Izv. Akad. Nauk Kazah. SSR Ser. Mat. Meh. 60(3) (1949), 101–105 (Russian, with Kazakh summary). MR 0045814
  • G. M. Goluzin, Some questions of the theory of univalent functions, Trudy Mat. Inst. Steklov. 27 (1949), 111 (Russian). MR 0042510
  • G. M. Goluzin, On mean values, Mat. Sbornik N.S. 25(67) (1949), 307–314 (Russian). MR 0032738
  • G. M. Goluzin, Some estimates for bounded functions, Mat. Sbornik N.S. 26(68) (1950), 7–18 (Russian). MR 0033351
  • G. M. Goluzin, On typically real functions, Mat. Sbornik N.S. 27(69) (1950), 201–218 (Russian). MR 0039060
  • G. M. Goluzin, On the theory of univalent functions, Mat. Sbornik N.S. 28(70) (1951), 351–358 (Russian). MR 0045815
  • G. M. Goluzin, On the theory of univalent functions, Mat. Sbornik N.S. 29(71) (1951), 197–208 (Russian). MR 0043208
  • G. M. Goluzin, On majorants of subordinate analytic functions. I, Mat. Sbornik N.S. 29(71) (1951), 209–224 (Russian). MR 0043209
  • G. M. Goluzin, On subordinate univalent functions, Trudy Mat. Inst. Steklov. 38 (1951), 68–71 (Russian). MR 0046432
  • G. M. Goluzin, Variational method in conformal mapping. IV, Mat. Sbornik N.S. 29(71) (1951), 455–468 (Russian). MR 0044641
  • G. M. Goluzin, On the parametric representation of functions univalent in a ring, Mat. Sbornik N.S. 29(71) (1951), 469–476 (Russian). MR 0047780
  • G. M. Goluzin, On majoration of subordinate analytic functions. II, Mat. Sbornik N.S. 29(71) (1951), 593–602 (Russian). MR 0044644
  • G. M. Goluzin, On the problem of coefficients of univalent functions, Doklady Akad. Nauk SSSR (N.S.) 81 (1951), 721–723 (Russian). MR 0045213
  • G. M. Goluzin, On a variational method in the theory of analytic functions, Leningrad. Gos. Univ. Učen. Zap. Ser. Mat. Nauk 144(23) (1952), 85–101 (Russian). MR 0077640
  • G. M. Goluzin, Geometricheskaya teoriya funktsiĭ kompleksnogo peremennogo, 2nd ed., Izdat. “Nauka”, Moscow, 1966 (Russian). Edited by V. I. Smirnov; With a supplement by N. A. Lebedev, G. V. Kuzmina and Ju. E. Alenicyn. MR 0219714
  • I. A. Aleksandrov, Parametricheskie prodolzheniya v teorii odnolistnykh funktsiĭ, Izdat. “Nauka”, Moscow, 1976 (Russian). MR 0480952
  • L. A. Aĭzenberg, Formuly Karlemana v kompleksnom analize, “Nauka” Sibirsk. Otdel., Novosibirsk, 1990 (Russian). Pervye prilozheniya. [First applications]. MR 1089612
  • G. M. Goluzin, Geometricheskaya teoriya funktsiĭ kompleksnogo peremennogo, 2nd ed., Izdat. “Nauka”, Moscow, 1966 (Russian). Edited by V. I. Smirnov; With a supplement by N. A. Lebedev, G. V. Kuzmina and Ju. E. Alenicyn. MR 0219714
  • G. P. Bakhtina, Variational methods and quadratic differentials in the problems on nonoverlapping domains, Thesis, Kiev, 1975, 12 pp. (Russian)
  • Roger W. Barnard and Alexander Yu. Solynin, Local variations and minimal area problem for Carathéodory functions, Indiana Univ. Math. J. 53 (2004), no. 1, 135–167. MR 2048187, DOI 10.1512/iumj.2004.53.2211
  • Roger W. Barnard, Kent Pearce, and Alexander Yu. Solynin, An isoperimetric inequality for logarithmic capacity, Ann. Acad. Sci. Fenn. Math. 27 (2002), no. 2, 419–436. MR 1922198
  • Roger W. Barnard, Kent Pearce, and Alexander Yu. Solynin, Area, width, and logarithmic capacity of convex sets, Pacific J. Math. 212 (2003), no. 1, 13–23. MR 2016565, DOI 10.2140/pjm.2003.212.13
  • V. P. Khavin and V. A. Bart, Szegő-Kolmogorov-Kreĭn theorems on a weighted trigonometric approximation, and Carleman-type formulas, Ukraïn. Mat. Zh. 46 (1994), no. 1-2, 100–127 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 46 (1994), no. 1-2, 101–132. MR 1294817, DOI 10.1007/BF01057004
  • L. de Branges, A proof of the Bieberbach conjecture, LOMI Preprints, no. E-5–84, Leningrad, 1984. (English)
  • Louis de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), no. 1-2, 137–152. MR 772434, DOI 10.1007/BF02392821
  • V. N. Dubinin, Change of harmonic measure in symmetrization, Mat. Sb. (N.S.) 124(166) (1984), no. 2, 272–279 (Russian). MR 746071
  • V. N. Dubinin, Transformation of functions and the Dirichlet principle, Mat. Zametki 38 (1985), no. 1, 49–55, 169 (Russian). MR 804180
  • V. N. Dubinin, A separating transformation of domains, and problems on extremal decomposition, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 168 (1988), no. Anal. Teor. Chisel i Teor. Funktsiĭ. 9, 48–66, 188 (Russian); English transl., J. Soviet Math. 53 (1991), no. 3, 252–263. MR 982483, DOI 10.1007/BF01303649
  • —, On the maximum of one conformal invariant, Preprint, Akad. Nauk SSSR Dal′nevost. Otdel., Inst. Prikl. Mat., Vladivostok, 1990. (Russian)
  • V. N. Dubinin, Symmetrization in the geometric theory of functions of a complex variable, Uspekhi Mat. Nauk 49 (1994), no. 1(295), 3–76 (Russian); English transl., Russian Math. Surveys 49 (1994), no. 1, 1–79. MR 1307130, DOI 10.1070/RM1994v049n01ABEH002002
  • V. N. Dubinin, Conformal mappings and inequalities for algebraic polynomials, Algebra i Analiz 13 (2001), no. 5, 16–43 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 13 (2002), no. 5, 717–737. MR 1882862
  • Peter L. Duren, Univalent functions, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 259, Springer-Verlag, New York, 1983. MR 708494
  • E. G. Emel′yanov, Some properties of moduli of families of curves, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 144 (1985), 72–82, 175 (Russian). Analytic number theory and the theory of functions, 6. MR 787415
  • E. G. Emel′yanov and G. V. Kuz′mina, Theorems on extremal partitioning in a family of systems of domains of different types, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 237 (1997), no. Anal. Teor. Chisel i Teor. Funkts. 14, 74–104, 229 (Russian, with Russian summary); English transl., J. Math. Sci. (New York) 95 (1999), no. 3, 2221–2239. MR 1691285, DOI 10.1007/BF02172467
  • S. I. Fedorov, On the maximum of a conformal invariant in a problem on nonoverlapping domains, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 112 (1981), 172–183, 202 (Russian). Analytic number theory and the theory of functions, 4. MR 644003
  • S. I. Fedorov, Chebotarev’s variational problem in the theory of the capacity of plane sets, and covering theorems for univalent conformal mappings, Mat. Sb. (N.S.) 124(166) (1984), no. 1, 121–139 (Russian). MR 743060
  • Carl H. FitzGerald and Ch. Pommerenke, The de Branges theorem on univalent functions, Trans. Amer. Math. Soc. 290 (1985), no. 2, 683–690. MR 792819, DOI 10.1090/S0002-9947-1985-0792819-9
  • O. M. Fomenko and G. V. Kuz′mina, The last 100 days of the Bieberbach conjecture, Math. Intelligencer 8 (1986), no. 1, 40–47. MR 823219, DOI 10.1007/BF03023920
  • G. M. Goluzin, Geometricheskaya teoriya funktsiĭ kompleksnogo peremennogo, 2nd ed., Izdat. “Nauka”, Moscow, 1966 (Russian). Edited by V. I. Smirnov; With a supplement by N. A. Lebedev, G. V. Kuzmina and Ju. E. Alenicyn. MR 0219714
  • Helmut Grunsky, Lectures on theory of functions in multiply connected domains, Studia Mathematica: Skript, vol. 4, Vandenhoeck & Ruprecht, Göttingen, 1978. MR 0463413
  • W. K. Hayman, Multivalent functions, 2nd ed., Cambridge Tracts in Mathematics, vol. 110, Cambridge University Press, Cambridge, 1994. MR 1310776, DOI 10.1017/CBO9780511526268
  • James A. Jenkins, On a problem of Gronwall, Ann. of Math. (2) 59 (1954), 490–504. MR 61170, DOI 10.2307/1969714
  • James A. Jenkins, Some theorems on boundary distortion, Trans. Amer. Math. Soc. 81 (1956), 477–500. MR 76862, DOI 10.1090/S0002-9947-1956-0076862-5
  • James A. Jenkins, On the existence of certain general extremal metrics, Ann. of Math. (2) 66 (1957), 440–453. MR 90648, DOI 10.2307/1969901
  • James A. Jenkins, On the existence of certain general extremal metrics. II, Tohoku Math. J. (2) 45 (1993), no. 2, 249–257. MR 1215927, DOI 10.2748/tmj/1178225919
  • James A. Jenkins, Univalent functions and conformal mapping, Reihe: Moderne Funktionentheorie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. MR 0096806
  • James A. Jenkins, On certain geometrical problems associated with capacity, Math. Nachr. 39 (1969), 349–356. MR 249594, DOI 10.1002/mana.19690390412
  • James A. Jenkins, The method of the extremal metric, The Bieberbach conjecture (West Lafayette, Ind., 1985) Math. Surveys Monogr., vol. 21, Amer. Math. Soc., Providence, RI, 1986, pp. 95–104. MR 875234, DOI 10.1090/surv/021/08
  • L. I. Kolbina, Some extremal problems in conformal mapping, Doklady Akad. Nauk SSSR (N.S.) 84 (1952), 865–868 (Russian). MR 0048582
  • L. I. Kolbina, Conformal mapping of the unit circle onto mutually nonoverlapping regions, Vestnik Leningrad. Univ. 10 (1955), no. 5, 37–43 (Russian). MR 0070723
  • Samuil L. Kruschkal and Reiner Kühnau, Quasikonforme Abbildungen—neue Methoden und Anwendungen, Teubner-Texte zur Mathematik [Teubner Texts in Mathematics], vol. 54, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1983 (German). With English, French and Russian summaries. MR 730760
  • V. O. Kuznetsov, Properties of associated quadratic differentials in some extremal problems, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 168 (1988), no. Anal. Teor. Chisel i Teor. Funktsiĭ. 9, 85–97, 188–189 (Russian); English transl., J. Soviet Math. 53 (1991), no. 3, 277–284. MR 982485, DOI 10.1007/BF01303651
  • G. V. Kuz′mina, Moduli of families of curves and quadratic differentials, Trudy Mat. Inst. Steklov. 139 (1980), 241 (Russian). MR 612632
  • G. V. Kuz′mina, On the problem of the maximum of the product of conformal radii of nonoverlapping domains, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 100 (1980), 131–145, 175–176 (Russian). Analytic number theory and the theory of functions, 3. MR 599943
  • G. V. Kuz′mina, On the extremal partitioning of the Riemann sphere, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 185 (1990), no. Anal. Teor. Chisel i Teor. Funktsiĭ. 10, 72–95, 184–185 (Russian); English transl., J. Soviet Math. 59 (1992), no. 6, 1180–1196. MR 1097590, DOI 10.1007/BF01374080
  • G. V. Kuz′mina, Methods of the geometric theory of functions. II, Algebra i Analiz 9 (1997), no. 5, 1–50 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 9 (1998), no. 5, 889–930. MR 1604397
  • G. V. Kuz′mina, The extremal metric method in problems of maximizing the product of powers of conformal radii of nonoverlapping domains in the presence of free parameters, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 302 (2003), no. Anal. Teor. Chisel i Teor. Funkts. 19, 52–67, 199 (Russian, with Russian summary); English transl., J. Math. Sci. (N.Y.) 129 (2005), no. 3, 3843–3851. MR 2023032, DOI 10.1007/s10958-005-0320-y
  • N. A. Lebedev, Majorizing region for the expression $I=\textrm {ln}(z^\lambda f’(z)^{1-\lambda })/f(z)^\lambda$ in the class $S$, Vestnik Leningrad. Univ. 10 (1955), no. 8, 29–41 (Russian). MR 0072213
  • N. A. Lebedev, Some estimates for functions regular and univalent in a circle, Vestnik Leningrad. Univ. 10 (1955), no. 11, 3–21 (Russian). MR 0074514
  • N. A. Lebedev, Printsip ploshchadeĭ v teorii odnolistnykh funktsiĭ, Izdat. “Nauka”, Moscow, 1975 (Russian). MR 0450540
  • Y. J. Leung, On the $N$th diameter problem in the class $\Sigma$, Complex Variables Theory Appl. 9 (1987), no. 2-3, 227–239. MR 923223, DOI 10.1080/17476938708814266
  • Y. J. Leung and G. Schober, The $N$th diameter problem in the class $\Sigma$, J. Analyse Math. 48 (1987), 247–266. MR 910011, DOI 10.1007/BF02790331
  • I. M. Milin, Odnolistnye funktsii i ortonormirovannye sistemy, Izdat. “Nauka”, Moscow, 1971 (Russian). MR 0369684
  • Jonathan R. Partington, Interpolation, identification, and sampling, London Mathematical Society Monographs. New Series, vol. 17, The Clarendon Press, Oxford University Press, New York, 1997. MR 1473224
  • Udo Pirl, Über die geometrische Gestalt eines Extremalkontinuums aus der Theorie der konformen Abbildung, Math. Nachr. 39 (1969), 297–312 (German). MR 254223, DOI 10.1002/mana.19690390408
  • G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, No. 27, Princeton University Press, Princeton, N. J., 1951. MR 0043486
  • Christian Pommerenke, Über die Subordination analytischer Funktionen, J. Reine Angew. Math. 218 (1965), 159–173 (German). MR 180669, DOI 10.1515/crll.1965.218.159
  • Ch. Pommerenke, On a variational method for univalent functions, Michigan Math. J. 17 (1970), 1–3. MR 255792
  • Christian Pommerenke, Univalent functions, Studia Mathematica/Mathematische Lehrbücher, Band XXV, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen. MR 0507768
  • Edgar Reich and Menahem Schiffer, Estimates for the transfinite diameter of a continuum, Math. Z. 85 (1964), 91–106. MR 174721, DOI 10.1007/BF01114881
  • A. C. Schaeffer and D. C. Spencer, Coefficient Regions for Schlicht Functions, American Mathematical Society Colloquium Publications, Vol. 35, American Mathematical Society, New York, N. Y., 1950. With a Chapter on the Region of the Derivative of a Schlicht Function by Arthur Grad. MR 0037908
  • Menahem Schiffer and Donald C. Spencer, Functionals of finite Riemann surfaces, Princeton University Press, Princeton, N. J., 1954. MR 0065652
  • A. Yu. Solynin, The dependence of the problem of moduli for a family of some classes of curves on parameters, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 144 (1985), 136–145, 177 (Russian). Analytic number theory and the theory of functions, 6. MR 787420
  • A. Yu. Solynin, Solution of the Pólya-Szegő isoperimetric problem, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 168 (1988), no. Anal. Teor. Chisel i Teor. Funktsiĭ. 9, 140–153, 190 (Russian); English transl., J. Soviet Math. 53 (1991), no. 3, 311–320. MR 982489, DOI 10.1007/BF01303655
  • A. Yu. Solynin, Moduli and extremal metric problems, Algebra i Analiz 11 (1999), no. 1, 3–86 (Russian); English transl., St. Petersburg Math. J. 11 (2000), no. 1, 1–65. MR 1691080
  • Alexander Yu. Solynin and Victor A. Zalgaller, An isoperimetric inequality for logarithmic capacity of polygons, Ann. of Math. (2) 159 (2004), no. 1, 277–303. MR 2052355, DOI 10.4007/annals.2004.159.277
  • Kurt Strebel, Quadratic differentials, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 5, Springer-Verlag, Berlin, 1984. MR 743423, DOI 10.1007/978-3-662-02414-0
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Bibliographic Information
  • G. V. Kuz′mina
  • Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
  • Email: kuzmina@pdmi.ras.ru
  • Received by editor(s): March 30, 2006
  • Published electronically: April 10, 2007

  • Dedicated: Dedicated to the 100th anniversary of Gennadiĭ Mikhaĭlovich Goluzin’s birth
  • © Copyright 2007 American Mathematical Society
  • Journal: St. Petersburg Math. J. 18 (2007), 347-372
  • MSC (2000): Primary 30-02, 30C55
  • DOI: https://doi.org/10.1090/S1061-0022-07-00954-5
  • MathSciNet review: 2255849