The harmonic map heat flow on conic manifolds

TL;DR

This paper investigates the harmonic map heat flow on manifolds with conic singularities, establishing short-term existence, uniqueness, and global solutions under certain curvature conditions using maximal regularity theory.

Contribution

It introduces a framework for analyzing harmonic map heat flow on conic manifolds, proving existence and uniqueness results that extend previous work to singular spaces.

Findings

Short time existence and uniqueness of solutions

Global solutions for nonpositive sectional curvature targets

Application of maximal regularity theory on conic manifolds

Abstract

In this article, we study the the harmonic map heat flow from a manifold with conic singularities to a closed manifold. In particular, we have proved the short time existence and uniqueness of solutions as well as the existence of global solutions into manifolds with nonpositive sectional curvature. These results are established in virtue of the maximal regularity theory on manifolds with conic singularities.