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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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An extremal method on arbitrary Riemann surfaces
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by Leo Sario PDF
Trans. Amer. Math. Soc. 73 (1952), 459-470 Request permission
References
  • Lars Ahlfors and Arne Beurling, Conformal invariants and function-theoretic null-sets, Acta Math. 83 (1950), 101–129. MR 36841, DOI 10.1007/BF02392634
    • H. Grunsky, Neue Abschätzungen zur konformen Abbildung ein- und mehrfach zusammen-hängender Bereiche, Schr. Math. Semin. Univ. Berlin vol. 1 (1932) pp. 95-140.
  • 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 32733
  • 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 43913
  • 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 38441
    • 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.
  • H. L. Royden, Some remarks on open Riemann surfaces, Ann. Acad. Sci. Fennicae Ser. A. I. Math.-Phys. 1951 (1951), no. 85, 8. MR 43914
  • Leo Sario, Über Riemannsche Flächen mit hebbarem Rand, Ann. Acad. Sci. Fennicae Ser. A. I. Math.-Phys. 1948 (1948), no. 50, 79 (German). MR 27859
  • 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
  • Leo Sario, A linear operator method on arbitrary Riemann surfaces, Trans. Amer. Math. Soc. 72 (1952), 281–295. MR 46442, DOI 10.1090/S0002-9947-1952-0046442-2
    • —, 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).
  • Leo Sario, Minimizing operators on subregions, Proc. Amer. Math. Soc. 4 (1953), 350–355. MR 54727, DOI 10.1090/S0002-9939-1953-0054727-5
    • —, Capacity of the boundary and of a boundary component, Ann. of Math. (to appear).
  • Menahem Schiffer, The span of multiply connected domains, Duke Math. J. 10 (1943), 209–216. MR 8259
  • 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 38443
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Additional Information
  • © Copyright 1952 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 73 (1952), 459-470
  • MSC: Primary 30.0X
  • DOI: https://doi.org/10.1090/S0002-9947-1952-0054053-8
  • MathSciNet review: 0054053