A local version of Bando's theorem on the real-analyticity of solutions to the Ricci flow

TL;DR

This paper extends Bando's theorem, which states that solutions to the Ricci flow are real-analytic on compact manifolds, to include smooth solutions on open subsets of manifolds, broadening the theorem's applicability.

Contribution

The paper introduces a local version of Bando's theorem, demonstrating real-analyticity of Ricci flow solutions on open domains, not just compact manifolds.

Findings

Real-analyticity holds locally for Ricci flow solutions

Extension of Bando's theorem to open domains

Broadens understanding of Ricci flow regularity

Abstract

It is a theorem of S. Bando that if $g(t)$ is a solution to the Ricci flow on a compact manifold $M$, then $(M, g(t))$ is real-analytic for each $t >0$. In this note, we extend his result to smooth solutions on open domains $U\subset M$.