Long-time existence of Yamabe flow on singular spaces with positive Yamabe constant

TL;DR

This paper proves the long-term existence of the normalized Yamabe flow on certain singular spaces with positive Yamabe constant, using parabolic Moser iteration to control solutions and scalar curvature.

Contribution

It extends the long-time existence results of Yamabe flow to manifolds with singularities, including stratified spaces, under certain analytic conditions.

Findings

Established long-time existence of Yamabe flow on singular spaces.

Developed a framework extending results to stratified spaces.

Used parabolic Moser iteration for uniform bounds.

Abstract

In this work we establish long-time existence of the normalized Yamabe flow with positive Yamabe constant on a class of manifolds that includes spaces with incomplete cone-edge singularities. We formulate our results axiomatically, so that our results extend to general stratified spaces as well, provided certain parabolic Schauder estimates hold. The central analytic tool is a parabolic Moser iteration, which yields uniform upper and lower bounds on both the solution and the scalar curvature.