Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A sharp condition for univalence in Euclidean spaces


Author: Julian Gevirtz
Journal: Proc. Amer. Math. Soc. 57 (1976), 261-265
MSC: Primary 26A57
MathSciNet review: 0404552
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ B \subset {K^k}$ be a ball. It is shown that if $ f:B \to {E^k}$ is a local homeomorphism for which the infinitesimal change in length is bounded above by $ M$ and for which the infinitesimal change in volume is bounded below by $ {m^k}$, where $ M/m \leq {2^{1\backslash k}}$, then $ f$ is univalent. This result is numerically sharp.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A57

Retrieve articles in all journals with MSC: 26A57


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0404552-3
PII: S 0002-9939(1976)0404552-3
Keywords: Univalent, local homeomorphism, quasi-isometric mapping
Article copyright: © Copyright 1976 American Mathematical Society