Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



Generalizations of Picard's theorem for Riemann surfaces

Author: Pentti Järvi
Journal: Trans. Amer. Math. Soc. 323 (1991), 749-763
MSC: Primary 30F25; Secondary 30D40
MathSciNet review: 1030508
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ D$ be a plane domain, $ E \subset D$ a compact set of capacity zero, and $ f$ a holomorphic mapping of $ D\backslash E$ into a hyperbolic Riemann surface $ W$. Then there is a Riemann surface $ W'$ containing $ W$ such that $ f$ extends to a holomorphic mapping of $ D$ into $ W'$. The same conclusion holds if hyperbolicity is replaced by the assumption that the genus of $ W$ be at least two. Furthermore, there is quite a general class of sets of positive capacity which are removable in the above sense for holomorphic mappings into Riemann surfaces of positive genus, except for tori.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30F25, 30D40

Retrieve articles in all journals with MSC: 30F25, 30D40

Additional Information

Article copyright: © Copyright 1991 American Mathematical Society