Neck analysis for biharmonic maps

TL;DR

This paper investigates the behavior of biharmonic maps in four dimensions, demonstrating the absence of neck formation during blow-up sequences and offering new proofs for key theorems in the field.

Contribution

It introduces a novel analysis of blow-up behavior for biharmonic maps and provides alternative proofs for the removable singularity and energy identity theorems.

Findings

No neck formation in blow-up sequences of biharmonic maps.

New proofs for the removable singularity theorem.

New proofs for the energy identity theorem.

Abstract

In this paper, we study the blow up of a sequence of (both extrinsic and intrinsic) biharmonic maps in dimension four with bounded energy and show that there is no neck in this process. Moreover, we apply the method to provide new proofs to the removable singularity theorem and energy identity theorem of biharmonic maps.