Biharmonic map heat flow into manifolds of nonpositive curvature |
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Authors: | Email author" target="_blank">Tobias?LammEmail author |
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Institution: | (1) Mathematisches Institut, Albert-Ludwigs Universität Freiburg, Eckerstr. 1, 79104 Freiburg, Germany |
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Abstract: | Let M
m
and N be two compact Riemannian manifolds without boundary. We consider the L
2 gradient flow for the energy
. If
and N has 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.Received: 27 March 2003, Accepted: 5 April 2004, Published online: 16 July 2004Mathematics Subject Classification (2000):
58E20, 58J35 |
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Keywords: | |
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