A sharp condition for univalence in Euclidean spaces
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- by Julian Gevirtz PDF
- Proc. Amer. Math. Soc. 57 (1976), 261-265 Request permission
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
- 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
- Fritz John, On quasi-isometric mappings. I, Comm. Pure Appl. Math. 21 (1968), 77–110. MR 222666, DOI 10.1002/cpa.3160210107
- Fritz John, On quasi,isometric mappings. II, Comm. Pure Appl. Math. 22 (1969), 265–278. MR 244741, DOI 10.1002/cpa.3160220209
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 261-265
- MSC: Primary 26A57
- DOI: https://doi.org/10.1090/S0002-9939-1976-0404552-3
- MathSciNet review: 0404552