Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Martin compactifications and quasiconformal mappings
HTML articles powered by AMS MathViewer

by Shigeo Segawa and Toshimasa Tada PDF
Proc. Amer. Math. Soc. 93 (1985), 242-244 Request permission

Abstract:

It is shown that there exists a quasiconformal mapping $T$ of a Riemann surface ${R_1}$ onto another ${R_2}$ such that $T$ cannot be extended to a homeomorphism of the Martin compactification $R_1^*$ of ${R_1}$ onto that $R_2^*$ of ${R_2}$.
References
  • Alano Ancona, Principe de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 4, 169–213, x (French, with English summary). MR 513885
  • Alano Ancona, Une propriété de la compactification de Martin d’un domaine euclidien, Ann. Inst. Fourier (Grenoble) 29 (1979), no. 4, ix, 71–90 (French, with English summary). MR 558589
  • Corneliu Constantinescu and Aurel Cornea, Ideale Ränder Riemannscher Flächen, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 32, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963 (German). MR 0159935
  • O. Lehto and K. I. Virtanen, Quasikonforme Abbildungen, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band 126, Springer-Verlag, Berlin-New York, 1965 (German). MR 0188434
  • H. L. Royden, Open Riemann surfaces, Ann. Acad. Sci. Fenn. Ser. A. I, no. 249/5 (1958), 13. MR 0100673
  • L. Sario and M. Nakai, Classification theory of Riemann surfaces, Die Grundlehren der mathematischen Wissenschaften, Band 164, Springer-Verlag, New York-Berlin, 1970. MR 0264064
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30F15, 30C60, 31A10
  • Retrieve articles in all journals with MSC: 30F15, 30C60, 31A10
Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 93 (1985), 242-244
  • MSC: Primary 30F15; Secondary 30C60, 31A10
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0770529-7
  • MathSciNet review: 770529