Title: Finite-time blow-up for the heat flow of pseudoharmonic maps

Authors: Ting-hui Chang and Shu-Cheng Chang

Issue: Volume 64 (2015), Issue 2, 441-470


In this paper, we consider the heat flow for pseudoharmonic maps from a closed pseudohermitian manifold $(M^{2n+1},J,\theta)$ into a compact Riemannian manifold $(N^m,g)$. In our pervious work, we proved global existence of the solution for the pseudoharmonic map heat flow, provided that the sectional curvature of the target manifold $N$ is nonpositive. In this present paper, we show that the solution of the pseudoharmonic map heat flow blows up in finite time if the initial map belongs to a nontrivial homotopy class and its initial energy is sufficiently small. As a consequence, we obtain global existence for the pseudoharmonic map heat flow without the curvature assumption on the target manifold.