Compactness results for sequences of approximate biharmonic maps

Christine Breiner and Tobias Lamm

Vol. 276 (2015), No. 1, 59–92

DOI: 10.2140/pjm.2015.276.59

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