Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

The Myers-Steenrod theorem for Finsler manifolds of low regularity


Authors: Vladimir S. Matveev and Marc Troyanov
Journal: Proc. Amer. Math. Soc. 145 (2017), 2699-2712
MSC (2010): Primary 53B40, 53C60, 35B65
DOI: https://doi.org/10.1090/proc/13407
Published electronically: February 10, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53B40, 53C60, 35B65

Retrieve articles in all journals with MSC (2010): 53B40, 53C60, 35B65


Additional Information

Vladimir S. Matveev
Affiliation: Institut für Mathematik, Friedrich-Schiller Universität Jena, 07737 Jena, Germany
Email: vladimir.matveev@uni-jena.de

Marc Troyanov
Affiliation: Section de Mathématiques, École Polytechnique Féderale de Lausanne, station 8, 1015 Lausanne, Switzerland
Email: marc.troyanov@epfl.ch

DOI: https://doi.org/10.1090/proc/13407
Keywords: Finsler metric, isometries, Myers-Steenrod theorem, Binet-Legendre metric
Received by editor(s): May 12, 2016
Received by editor(s) in revised form: July 27, 2016
Published electronically: February 10, 2017
Additional Notes: The authors thank the Friedrich-Schiller-Universität Jena, EPFL and the Swiss National Science Foundation for their support.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2017 American Mathematical Society