Uniqueness of tangent cones for biharmonic maps with isolated singularities

Youmin Chen and Hao Yin

Vol. 299 (2019), No. 2, 401–426

DOI: 10.2140/pjm.2019.299.401

Abstract

We study the problem of uniqueness of a tangent cone for minimizing extrinsic biharmonic maps. Following the celebrated result of Simon, we prove that if the target manifold is a compact analytic submanifold in ${ℝ}^p$ and if there is one tangent map whose singularity set consists of the origin only, then this tangent map is unique.

Keywords

biharmonic map, tangent map

Mathematical Subject Classification 2010

Primary: 58E20

Secondary: 35J30

Milestones

Received: 5 May 2017

Revised: 15 May 2018

Accepted: 24 June 2018

Published: 21 May 2019