Vol. 5, No. 1, 2012

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Energy identity for intrinsically biharmonic maps in four dimensions

Peter Hornung and Roger Moser

Vol. 5 (2012), No. 1, 61–80
Abstract

Let u be a mapping from a bounded domain S 4 into a compact Riemannian manifold N. Its intrinsic biharmonic energy E2(u) is given by the squared L2-norm of the intrinsic Hessian of u. We consider weakly converging sequences of critical points of E2. Our main result is that the energy dissipation along such a sequence is fully due to energy concentration on a finite set and that the dissipated energy equals a sum over the energies of finitely many entire critical points of E2.

Keywords
biharmonic map, energy identity, bubbling
Mathematical Subject Classification 2000
Primary: 58E20, 35J35
Milestones
Received: 4 November 2009
Revised: 24 November 2010
Accepted: 25 January 2011
Published: 25 June 2012
Authors
Peter Hornung
Max-Planck-Institut für Mathematik in den Naturwissenschaften
Inselstraße. 22
04103 Leipzig
Germany
Roger Moser
Department of Mathematical Sciences
University of Bath
Bath
BA2 7AY
United Kingdom