On the p-pseudoharmonic map heat flow

TL;DR

This paper studies the heat flow for p-pseudoharmonic maps from Sasakian manifolds to Riemannian manifolds, proving global existence and convergence under curvature or energy conditions.

Contribution

It establishes the global existence and convergence of the p-pseudoharmonic map heat flow under new curvature and energy conditions.

Findings

Global existence under nonpositive curvature of N

Asymptotic convergence when initial p-energy is small

Results extend understanding of pseudoharmonic map heat flow

Abstract

In this paper, we consider the heat flow for p-pseudoharmonic maps from a closed Sasakian manifold M into a compact Riemannian manifold N. We prove global existence and asymptotic convergence of the solution for the p-pseudoharmonic map heat flow, provided that the sectional curvature of the target manifold N is nonpositive. Moreover, without the curvature assumption on the target manifold, we obtain global existence and asymptotic convergence of the p-pseudoharmonic map heat flow as well when its initial p-energy is sufficiently small.