Abstract
Let ( M m , g) and ( N n , h) ( m⩾2) be two compact Riemannian manifolds without boundary. When Riem N ⩽0, we show the global existence of a weak solution of the heat equation for p-harmonic maps ( p>1) and the convergence of this solution at infinity to a regular weakly p-harmonic map; so generalizing the result of Eells–Sampson for harmonic maps to the case that p>1.
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