Heat flows of harmonic maps with potential into manifolds with nonpositive curvature

摘要

In this paper, we discuss the heat flows of harmonic maps with potential from compact manifolds with boundary into manifolds with nonpositive curvature. We obtain precise conditions which link the Hessian of the potential function and the spectrums of the domain manifolds and ensure the existence of global solutions and their convergence. An example is given to show the sharpness of the condition.