The Myers-Steenrod Theorem For Finsler Manifolds Of Low Regularity

We prove a version of Myers-Steenrod's theorem for Finsler manifolds under the minimal regularity hypothesis. In particular we show that an isometry between C-k,C-alpha-smooth (or partially smooth) Finsler metrics, with k + alpha > 0, k is an element of N boolean OR {0}, and 0 <= alpha <= 1 is necessarily a diffeomorphism of class C-k+1,C-alpha. A generalization of this result to the case of Finsler 1-quasiconformal mapping is given. The proofs are based on the reduction of the Finslerian problems to Riemannian ones with the help of the Binet-Legendre metric.


Published in:
Proceedings Of The American Mathematical Society, 145, 6, 2699-2712
Year:
2017
Publisher:
Providence, Amer Mathematical Soc
ISSN:
0002-9939
Keywords:
Laboratories:




 Record created 2017-05-30, last modified 2018-09-13


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