Convergence rate of the weighted Yamabe flow

TL;DR

This paper investigates the convergence rate of the weighted Yamabe flow, a geometric flow used to address the weighted Yamabe problem on smooth metric measure spaces, extending previous work on the unweighted case.

Contribution

It provides new insights into the convergence behavior of the weighted Yamabe flow, building upon prior results for the classical Yamabe flow.

Findings

Established convergence rate estimates for the weighted Yamabe flow

Extended known results from the unweighted to the weighted setting

Provided analytical tools for studying geometric flows on measure spaces

Abstract

The weighted Yamabe flow was the geometric flow introduced to study the weighted Yamabe problem on smooth metric measure spaces. Carlotto, Chodosh and Rubinstein have studied the convergence rate of the Yamabe flow. Inspired by their result, we study in this paper the convergence rate of the weighted Yamabe flow.