Ricci flow on Finsler manifolds

TL;DR

This paper establishes the short-time existence and uniqueness of Ricci flow solutions on Finsler manifolds, extending Ricci flow theory beyond Riemannian geometry with specific results for isotropic cases.

Contribution

It proves theorems on short-time existence and uniqueness of Ricci flow on Finsler manifolds, a novel extension of geometric flow theory.

Findings

Existence of Ricci flow solutions on Finsler manifolds

Uniqueness of solutions for isotropic Finsler manifolds

Illustrative examples demonstrating the results

Abstract

This paper investigates the short-time existence and uniqueness of Ricci flow solutions on Finsler manifolds. The main results of this paper are theorems demonstrating the short-time existence of the flow solution for $n$-dimensional Finsler manifolds and the uniqueness of the solution for isotropic Finsler manifolds. Two examples are also presented to illustrate the results.