Gradient Flow on Finsler manifold

TL;DR

This paper provides an overview of curvature functionals in Finsler geometry and introduces gradient flows on Finsler manifolds, aiming to deepen understanding of geometric analysis in this context.

Contribution

It offers a comprehensive overview of curvature functionals and proposes new gradient flows tailored for Finsler manifolds, expanding the tools available for geometric analysis.

Findings

Introduction of new gradient flows on Finsler manifolds

Analysis of curvature functionals in Finsler geometry

Potential applications in geometric analysis

Abstract

Studying various functionals and associated gradient ows are known problems in differential geometry. The perpose of this article is to provide a general overview of curvature functionals in Finsler geometry and use their information for introducing different gradient ows on Finsler manifolds.