On the p-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.