A simple proof of the short-time existence and uniqueness for Ricci flow

TL;DR

This paper provides a straightforward proof of the local existence and uniqueness of Ricci flow on closed Einstein manifolds, and introduces a new framework for analyzing the space of Riemannian metrics on compact manifolds.

Contribution

It offers a simplified proof of Ricci flow's local existence and uniqueness on Einstein manifolds and proposes a novel setting for studying Riemannian metrics.

Findings

Proof of short-time existence and uniqueness for Ricci flow on Einstein manifolds

Introduction of a new framework for the space of Riemannian metrics

Simplification of existing proofs in Ricci flow theory

Abstract

In this short note, we give simple proof of the Ricci flow's local existence and uniqueness on closed Einstein manifolds. We suggest a new setting for studying the space of Riemannian metrics on a compact manifold.