Two-dimensional Ricci flow as a stochastic process

TL;DR

This paper demonstrates that the Ricci flow on a two-dimensional Riemannian manifold can be represented as a stochastic process driven by a Wiener (Brownian motion) process.

Contribution

It establishes a novel stochastic interpretation of the two-dimensional Ricci flow, linking geometric evolution to stochastic analysis.

Findings

Ricci flow corresponds to a Wiener process in 2D

Provides a probabilistic framework for Ricci flow

Bridges differential geometry and stochastic processes

Abstract

We prove that, for a two-dimensional Riemannian manifold, the Ricci flow is obtained by a Wiener process.