Biharmonic map heat flow into manifolds of nonpositive curvature

Lamm, Tobias
April 2005
Calculus of Variations & Partial Differential Equations;Apr2005, Vol. 22 Issue 4, p421
Academic Journal
LetMm andNbe two compact Riemannian manifolds without boundary. We consider theL2 gradient flow for the energy. IfandNhas nonpositive sectional curvature we show that the biharmonic map heat flow exists for all time, and that the solution subconverges to a smooth harmonic map as time goes to infinity. This reproves the celebrated theorem of Eells and Sampson [6] on the existence of harmonic maps in homotopy classes for domain manifolds with dimension less than or equal to 4.


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