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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
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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?)

  • [1] Julian Gevirtz, On the univalence of quasi-isometric mappings, Rev. Colombiana Mat. 7 (1973), 125–132. Collection of articles dedicated to the memory of Luis I. Soriano (1903–1973). MR 0426024
  • [2] Fritz John, On quasi-isometric mappings. I, Comm. Pure Appl. Math. 21 (1968), 77–110. MR 0222666
  • [3] Fritz John, On quasi,isometric mappings. II, Comm. Pure Appl. Math. 22 (1969), 265–278. MR 0244741

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0404552-3
Keywords: Univalent, local homeomorphism, quasi-isometric mapping
Article copyright: © Copyright 1976 American Mathematical Society