Hamilton's Ricci Flow on Finsler Spaces

TL;DR

This paper establishes the short-time existence of solutions to Hamilton's Ricci flow on Finsler spaces by defining and analyzing a Finslerian Ricci-DeTurck flow, extending Ricci flow theory to Finsler geometry.

Contribution

It introduces a Finslerian Ricci-DeTurck flow and proves short-time existence of solutions, advancing the understanding of Ricci flow in Finsler geometry.

Findings

Existence of short-time solutions to Hamilton's Ricci flow on Finsler spaces.

Definition and analysis of Finslerian Ricci-DeTurck flow.

Method to pull back solutions to the original Finsler Ricci flow.

Abstract

Recently, we have studied evolution of a family of Finsler metrics along Finsler Ricci flow and proved its convergence in short time. Here, existence of solutions to the so called Hamilton Ricci flow on Finsler spaces is studied and a short time solution is found. To this end the Finslerian Ricci-DeTurck flow on Finsler spaces is defined and existence of its solution in short time is proved. Next, this solution is pulled back to determine a short time solution to the Hamilton Ricci flow on underlying Finsler space.