Compactness results for sequences of approximate biharmonic maps

Abstract

In this article, we prove energy quantization for approximate (intrinsic and extrinsic) biharmonic maps into spheres where the approximate map is in L log L. Moreover, we demonstrate that if the L log L norm of the approximate maps does not concentrate, the image of the bubbles are connected without necks.

On the Finite Time Blow-up of Biharmonic Map Flow in Dimension Four

“…Remark 1.3. Recently, we notice that Breiner and Lamm [2] proved a no neck theorem for a sequence of biharmonic maps with bi-tension fields in L log L when the target manifold is a sphere. In this paper, by approximate biharmonic maps, we mean bi-tension field is bounded in L 2 .…”