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An extremal method on arbitrary Riemann surfaces
Author:
Leo Sario
Journal:
Trans. Amer. Math. Soc. 73 (1952), 459-470
MSC:
Primary 30.0X
MathSciNet review:
0054053
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References |
Similar Articles |
Additional Information
- [1]
Lars
Ahlfors and Arne
Beurling, Conformal invariants and function-theoretic
null-sets, Acta Math. 83 (1950), 101–129. MR 0036841
(12,171c)
- [2]
H. Grunsky, Neue Abschätzungen zur konformen Abbildung ein- und mehrfach zusammen-hängender Bereiche, Schr. Math. Semin. Univ. Berlin vol. 1 (1932) pp. 95-140.
- [3]
Olli
Lehto, On the existence of analytic functions with a finite
Dirichlet integral, Ann. Acad. Sci. Fennicae. Ser. A. I. Math.-Phys.
1949 (1949), no. 67, 7. MR 0032733
(11,338d)
- [4]
Olli
Lokki, Beiträge zur Theorie der analytischen und harmonischen
Funktionen mit endlichem Dirichletintegral, Ann. Acad. Sci. Fennicae.
Ser. A. I. Math.-Phys. 1951 (1951), no. 92, 11
(German). MR
0043913 (13,338h)
- [5]
Michel
Parreau, Sur certaines classes de fonctions analytiques uniformes
sur les surfaces de Riemann, C. R. Acad. Sci. Paris
231 (1950), 751–753 (French). MR 0038441
(12,402c)
- [6]
R. de Possel, Sur quelques propriétés de la représentation conforme des domains multiplement connexes, en relation avec le théorème des fentes parallèles, Math. Ann. vol. 107 (1932) pp. 496-504.
- [7]
H.
L. Royden, Some remarks on open Riemann surfaces, Ann. Acad.
Sci. Fennicae. Ser. A. I. Math.-Phys. 1951 (1951),
no. 85, 8. MR 0043914
(13,339a)
- [8]
Leo
Sario, Über Riemannsche Flächen mit hebbarem Rand,
Ann. Acad. Sci. Fennicae. Ser. A. I. Math.-Phys. 1948
(1948), no. 50, 79 (German). MR 0027859
(10,365c)
- [9]
Leo
Sario, Sur la classification des surfaces de Riemann, Den 11te
Skandinaviske Matematikerkongress, Trondheim, 1949, Johan Grundt Tanums
Forlag, Oslo, 1952, pp. 229–238 (French). MR 0054052
(14,863a)
- [10]
Leo
Sario, A linear operator method on arbitrary
Riemann surfaces, Trans. Amer. Math. Soc.
72 (1952),
281–295. MR 0046442
(13,735c), http://dx.doi.org/10.1090/S0002-9947-1952-0046442-2
- [11]
-, Construction of functions with prescribed properties on Riemann surfaces, Conference on Riemann Surfaces in Commemoration of the Hundredth Anniversary of Riemann's Inaugural-Dissertation, Princeton, 1951, Annals of Mathematics Studies (to appear).
- [12]
Leo
Sario, Minimizing operators on
subregions, Proc. Amer. Math. Soc. 4 (1953), 350–355. MR 0054727
(14,969g), http://dx.doi.org/10.1090/S0002-9939-1953-0054727-5
- [13]
-, Capacity of the boundary and of a boundary component, Ann. of Math. (to appear).
- [14]
Menahem
Schiffer, The span of multiply connected domains, Duke Math.
J. 10 (1943), 209–216. MR 0008259
(4,271a)
- [15]
K.
I. Virtanen, Über die Existenz von beschränkten
harmonischen Funktionen auf offenen Riemannschen Flächen, Ann.
Acad. Sci. Fennicae. Ser. A. I. Math.-Phys. 1950 (1950),
no. 75, 8 (German). MR 0038443
(12,403b)
- [1]
- L. Ahlfors and A. Beurling, Conformal invariants and function-theoretic null-seis, Acta Math. vol. 83 (1950) pp. 101-129. MR 0036841 (12:171c)
- [2]
- H. Grunsky, Neue Abschätzungen zur konformen Abbildung ein- und mehrfach zusammen-hängender Bereiche, Schr. Math. Semin. Univ. Berlin vol. 1 (1932) pp. 95-140.
- [3]
- O. Lehto, On the existence of analytic functions with a finite Dirichlet integral, Annales Academiae Scientiarum Fennicae Ser. A.I. no. 67 (1949) pp. 1-7. MR 0032733 (11:338d)
- [4]
- O. Lokki, Beiträge zur Theorie der analytischen und harmonischen Functionen mit endlichem Dirichlet-integral, Annales Academiae Scientiarum Fennicae Ser. A.I. no. 92 (1951) pp. 1-10. MR 0043913 (13:338h)
- [5]
- M. Parreau, Sur certaines classes de fonctions analytiques uniformes sur les surfaces de Riemann, C. R. Acad. Sci. Paris vol. 231 (1950) pp. 751-753. MR 0038441 (12:402c)
- [6]
- R. de Possel, Sur quelques propriétés de la représentation conforme des domains multiplement connexes, en relation avec le théorème des fentes parallèles, Math. Ann. vol. 107 (1932) pp. 496-504.
- [7]
- H. L. Royden, Some remarks on open Riemann surfaces, Annales Academiae Scientiarum Fennicae Ser. A.I. no. 85 (1951) pp. 1-8. MR 0043914 (13:339a)
- [8]
- L. Sario, Ueber Riemannsche Flächen mit hebbarem Rand, Annales Academiae Scientiarum Fennicae Ser. A.I. no. 50 (1948) pp. 1-79. MR 0027859 (10:365c)
- [9]
- -, Sur la classification des surfaces de Riemann, Congr. Math. Scand. Trondheim, 1949, pp. 229-238. MR 0054052 (14:863a)
- [10]
- -, A linear operator method on arbitrary Riemann surfaces, Trans. Amer. Math. Soc. vol. 72 (1952) pp. 281-295. MR 0046442 (13:735c)
- [11]
- -, Construction of functions with prescribed properties on Riemann surfaces, Conference on Riemann Surfaces in Commemoration of the Hundredth Anniversary of Riemann's Inaugural-Dissertation, Princeton, 1951, Annals of Mathematics Studies (to appear).
- [12]
- -, Minimizing operators on subregions, Proc. Amer. Math. Soc. (to appear). MR 0054727 (14:969g)
- [13]
- -, Capacity of the boundary and of a boundary component, Ann. of Math. (to appear).
- [14]
- M. Schiffer, The span of multiply connected domains, Duke Math. J. vol. 10 (1943) pp. 209-216. MR 0008259 (4:271a)
- [15]
- K. I. Virtanen, Ueber die Existenz von beschränkten harmonischen Funktionen auf offenen Riemannschen Flächen, Annales Academiae Scientiarum Fennicae Ser. A.I. No. 75 (1950) pp. 1-8. MR 0038443 (12:403b)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1952-0054053-8
PII:
S 0002-9947(1952)0054053-8
Article copyright:
© Copyright 1952 American Mathematical Society
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