#### Vol. 276, No. 1, 2015

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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