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International Mathematics Research Papers (2005) 2005:351-402, doi:10.1155/IMRP.2005.351
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Copyright © 2005 Hindawi Publishing Corporation. All rights reserved.

The blowup behavior of the biharmonic map heat flow in four dimensions

Roger Moser

We study the (intrinsic) biharmonic map heat flow on a four-dimensional domain into a compact Riemannian manifold. We examine its behavior as the first finite-time singularity is approached. At each singular point, we find either a harmonic sphere or a biharmonic map bubbling-off. A further description of the singular set is also given. The proofs rely to a large extent on a blowup analysis of sequences of maps with uniformly bounded energy.


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