Narrow Results

In this paper, we consider the heat flow for $p$-pseudoharmonic maps from a closed Sasakian manifold $(M^{2n+1},J,𝜃)$ into a compact Riemannian manifold $(N^m,g_{ij})$. 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 non-positive. 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.