Heat flow for VT harmonic map from compact manifold

TL;DR

This paper establishes the existence of solutions for VT harmonic maps and geodesics from compact Riemannian manifolds using heat flow methods, expanding understanding of these geometric flows.

Contribution

It introduces new existence results for VT harmonic maps and geodesics under specific conditions, utilizing heat flow techniques.

Findings

Existence of Dirichlet problem solutions for VT harmonic maps.

Existence of VT geodesics under certain conditions.

Application of heat flow method to geometric analysis.

Abstract

In this paper, we obtain the existence of Dirichlet problem for VT harmonic map from compact Riemannian manifold with or without boundary into compact manifold via the heat flow method. We also obtain the existence of V T geodesics uncer certain conditions on T.