Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Martin compactifications and quasiconformal mappings


Authors: Shigeo Segawa and Toshimasa Tada
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] A. Ancona, Principe de Harnack a la frontière et théorème de Fatou pour opérateur elliptique dans un domaine lipschitzien, Ann. Inst. Fourier (Grenoble) 28 (1978), 169-213. MR 513885 (80d:31006)
  • [2] -, Une propriété de la compactification de Martin d'un domaine euclidien, Ann. Inst. Fourier (Grenoble) 29 (1979), 71-90. MR 558589 (81f:31013)
  • [3] C. Constantinescu and A. Cornea, Ideale Ränder Riemannscher Flächen, Springer-Verlag, Berlin and New York, 1963. MR 0159935 (28:3151)
  • [4] O. Lehto and K. I. Virtanen, Quasikonforme Abbildungen, Springer-Verlag, Berlin and New York, 1965. MR 0188434 (32:5872)
  • [5] H. L. Royden, Open Riemann surfaces, Ann. Acad. Sci. Fenn. Ser. A I No. 249 (1958), 13 pp. MR 0100673 (20:7102)
  • [6] L. Sario and M. Nakai, Classification theory of Riemann surfaces, Springer-Verlag, Berlin and New York, 1970. MR 0264064 (41:8660)

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

DOI: https://doi.org/10.1090/S0002-9939-1985-0770529-7
Keywords: Martin compactification, quasiconformal mapping
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society