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• [3] E. David Callender, Hölder continuity of 𝑛-dimensional quasi-conformal mappings, Pacific J. Math. 10 (1960), 499–515. MR 0118794 (22 #9564)
• [4] James A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396–414. MR 1501880, http://dx.doi.org/10.1090/S0002-9947-1936-1501880-4
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• [6] F. W. Gehring, The definitions and exceptional sets for quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I No. 281 (1960), 28. MR 0124488 (23 #A1800)
• [7] F. W. Gehring, Rings and quasiconformal mappings in space, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 98–105. MR 0125964 (23 #A3261)
• [8] F. W. Gehring, A remark on the moduli of rings, Comment. Math. Helv. 36 (1961), 42–46. MR 0140682 (25 #4097)
• [9] F. W. Gehring, Symmetrization of rings in space, Trans. Amer. Math. Soc. 101 (1961), 499–519. MR 0132841 (24 #A2677), http://dx.doi.org/10.1090/S0002-9947-1961-0132841-2
• [10] F. W. Gehring and Jussi Väisälä, On the geometric defintion for quasiconformal mappings, Comment. Math. Helv. 36 (1961), 19–32. MR 0140684 (25 #4099)
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• [13] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, 1934.
• [14] Eberhard Hopf, Über den funktionalen, insbesondere den analytischen Charakter der Lösungen elliptischer Differentialgleichungen zweiter Ordnung, Math. Z. 34 (1932), no. 1, 194–233 (German). MR 1545250, http://dx.doi.org/10.1007/BF01180586
• [15] H. Lebesgue, Sur le problème de Dirichlet, Rend. Circ. Mat. Palermo 24 (1907), 371-402.
• [16] Charles Loewner, On the conformal capacity in space, J. Math. Mech. 8 (1959), 411–414. MR 0104785 (21 #3538)
• [17] D. Menchoff, Sur une généralisation d'un théorème de M. H. Bohr, Mat. Sb. 44 (1937), 339-354.
• [18] Akira Mori, On an absolute constant in the theory of quasi-conformal mappings, J. Math. Soc. Japan 8 (1956), 156–166. MR 0079091 (18,27e)
• [19] Akira Mori, On quasi-conformality and pseudo-analyticity, Trans. Amer. Math. Soc. 84 (1957), 56–77. MR 0083024 (18,646c), http://dx.doi.org/10.1090/S0002-9947-1957-0083024-5
• [20] C. B. Morrey Jr., Second-order elliptic systems of differential equations, Contributions to the theory of partial differential equations, Annals of Mathematics Studies, no. 33, Princeton University Press, Princeton, N. J., 1954, pp. 101–159. MR 0068091 (16,827e)
• [21] Jürgen Moser, A new proof of De Giorgi’s theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math. 13 (1960), 457–468. MR 0170091 (30 #332)
• [22] Rolf Nevanlinna, On differentiable mappings, Analytic functions, Princeton Univ. Press, Princeton, N.J., 1960, pp. 3–9. MR 0116280 (22 #7075)
• [23] Albert Pfluger, Quasikonforme Abbildungen und logarithmische Kapazität, Ann. Inst. Fourier Grenoble 2 (1950), 69–80 (1951) (German). MR 0044640 (13,453f)
• [24] T. Rado and P. V. Reichelderfer, Continuous transformations in analysis. With an introduction to algebraic topology, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Bd. LXXV, Springer-Verlag, Berlin, 1955. MR 0079620 (18,115c)
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• [26] Ju. G. Rešetnjak, On conformal mappings of a space, Soviet Math. Dokl. 1 (1960), 153–155. MR 0119169 (22 #9935)
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• [29] Jussi Väisälä, On quasiconformal mappings of a ball, Ann. Acad. Sci. Fenn. Ser. A I No. 304 (1961), 7. MR 0140686 (25 #4100b)

Bibliography

[1]

L. V. Ahlfors, On quasiconformal mappings, J. Analyse Math. 3 (1954), 1-58. MR 0064875 (16:348d)

[2]

A. Beurling and L. V. Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956), 125-142. MR 0086869 (19:258c)

[3]

E. D. Callender, Hölder continuity of N-dimensional quasi-conformal mappings, Pacific J. Math. 10 (1960), 499-515. MR 0118794 (22:9564)

[4]

J. A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), 396-414. MR 1501880

[5]

H. Federer, Curvature measures, Trans. Amer. Math. Soc. 93 (1959), 418-491. MR 0110078 (22:961)

[6]

F. W. Gehring, The definitions and exceptional sets for quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A 281 (1960), 1-28. MR 0124488 (23:A1800)

[7]

-, Rings and quasiconformal mappings in space, Proc. Nat. Acad. Sci. U.S.A. 47 (1961),98-105. MR 0125964 (23:A3261)

[8]

-, A remark on the moduli of rings, Comment. Math. Helv. 36 (1961), 42-46. MR 0140682 (25:4097)

[9]

-, Symmetrization of rings in space, Trans. Amer. Math. Soc. 101 (1961), 499-519. MR 0132841 (24:A2677)

[10]

F. W. Gehring and J. Väisälä, On the geometric definition for quasiconformal mappings, Comment. Math. Helv. 36 (1961), 19-32. MR 0140684 (25:4099)

[11]

E. de Giorgi, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Nat. 3 (1957), 25-43. MR 0093649 (20:172)

[12]

W. Gross, Über das Flächenmass von Punktmengen, Monatsh. Math. 29 (1918), 145-176.

[13]

G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, 1934.

[14]

E. Hopf, Über den funktionalen, inbesondere den analytischen Charakter der Lösungen elliptischer Differentialgleichungen zweiter Ordnung, Math. Z. 34 (1932), 194-233. MR 1545250

[15]

H. Lebesgue, Sur le problème de Dirichlet, Rend. Circ. Mat. Palermo 24 (1907), 371-402.

[16]

C. Loewner, On the conformal capacity in space, J. Math. Mech. 8 (1959), 411-414. MR 0104785 (21:3538)

[17]

D. Menchoff, Sur une généralisation d'un théorème de M. H. Bohr, Mat. Sb. 44 (1937), 339-354.

[18]

A. Mori, On an absolute constant in the theory of quasi-conformal mappings, J. Math. Soc. Japan 8 (1956), 156-166. MR 0079091 (18:27e)

[19]

-, On quasi-conformality and pseudo-analyticity, Trans. Amer. Math. Soc. 84 (1957), 56-77. MR 0083024 (18:646c)

[20]

C. B. Morrey, Second order elliptic systems of differential equations, Annals of Mathematics Studies No. 33, pp. 101-159, Princeton Univ. Press, Princeton, N. J. 1954. MR 0068091 (16:827e)

[21]

J. Moser, A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math. 13 (1960), 457-468. MR 0170091 (30:332)

[22]

R. Nevanlinna, On differentiable mappings, Analytic Functions, pp. 3-9, Princeton Univ. Press, Princeton, N. J., 1960. MR 0116280 (22:7075)

[23]

A. Pfluger, Quasikonforme Abbildungen und logarithmische Kapazität, Ann. Inst. Fourier Grenoble 2 (1950), 69-80. MR 0044640 (13:453f)

[24]

T. Radó and P. V. Reichelderfer, Continuous transformations in analysis, Springer-Verlag, Berlin, 1955. MR 0079620 (18:115c)

[25]

Yu. Rešetnyak, A sufficient condition for Hölder continuity of a mapping, Soviet Math. Dokl. 1 (1960), 76-78. MR 0122941 (23:A273)

[26]

-, On conformal mappings of a space, Soviet Math. Dokl. 1 (1960), 153-155. MR 0119169 (22:9935)

[27]

S. Saks, Theory of the integral, Warsaw, 1937.

[28]

J. Väisälä, On quasiconformal mappings in space, Ann. Acad. Sci. Fenn. Ser. A 298 (1961), 1-36. MR 0140685 (25:4100a)

[29]

-, On quasiconformal mappings of a ball, Ann. Acad. Sci. Fenn. Ser. A 304 (1961), 1-7. MR 0140686 (25:4100b)