Conformal boundary rigidity for simple Finsler metrics

Kelvin Lam; Hanming Zhou

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arXiv · 2609.09527

Conformal boundary rigidity for simple Finsler metrics

Kelvin Lam·Hanming Zhou

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Abstract

In this paper we prove that simple Finsler manifolds are conformally stable. Given a simple Finsler manifold and a class of conformal factors, we characterize the singularity of their induced boundary distance functions which allows us to define an appropiate $H^2$ norm. We then obtain a stability estimate with respect to this Sobolev norm and the $L^2$ norm on the class of the conformal factors. To prove the main theorems, we adapt the classical integration by parts technique employed by Mukhometov \cite{Muhometov} to the Finsler setting.

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BibTeX RIS

Kelvin Lam, Hanming Zhou. 2026-09-08. Conformal boundary rigidity for simple Finsler metrics. https://arxiv.org/abs/2609.09527

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