A Generalization of Eells-Sampson's Theorem (Journal of Partial Differential Equations, 2020)
We generalize the well-known Eells-Sampson's theorem on the global existence and convergence for the heat flow of harmonic maps. The assumption that the curvature of the target manifold N be nonpoeitive is replaced by the weaker one requiring that the universal cover \tilde{N} admit a strictly convex function with quadratic growth.