The Myers-Steenrod theorem for Finsler manifolds of low regularity

Matveev, Vladimir; Troyanov, Marc

doi:10.1090/proc/13407

The Myers-Steenrod theorem for Finsler manifolds of low regularity
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by Vladimir S. Matveev and Marc Troyanov PDF

Proc. Amer. Math. Soc. 145 (2017), 2699-2712 Request permission

Abstract:

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 $C^{k,\alpha }$-smooth (or partially smooth) Finsler metrics, with $k+\alpha >0$, $k\in \mathbb {N} \cup \{0\}$, and $0 \leq \alpha \leq 1$ is necessarily a diffeomorphism of class $C^{k+1,\alpha }$. 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.

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