Vol. 276, No. 1, 2015

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ISSN: 0030-8730
Compactness results for sequences of approximate biharmonic maps

Christine Breiner and Tobias Lamm

Vol. 276 (2015), No. 1, 59–92
Abstract

We will prove energy quantization for approximate (intrinsic and extrinsic) biharmonic maps into spheres where the approximate map is in LlogL. Moreover, we demonstrate that if the LlogL norm of the approximate maps does not concentrate, the images of the bubbles are connected without necks.

Keywords
harmonic maps, biharmonic maps, bubbling, energy quantization
Mathematical Subject Classification 2010
Primary: 35J60, 35J48
Secondary: 58E20
Milestones
Received: 30 December 2013
Revised: 4 July 2014
Accepted: 3 December 2014
Published: 1 July 2015
Authors
Christine Breiner
Department of Mathematics
Fordham University
Bronx, NY 10458
United States
Tobias Lamm
Institute for Analysis
Karlsruhe Institute of Technology
Kaiserstraße 89-93
D-76133 Karlsruhe
Germany