Vol. 299, No. 2, 2019

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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 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
Authors
Youmin Chen
School of mathematical sciences
University of Science and Technology of China
Hefei
China
Hao Yin
School of Mathematical Sciences
University of Science and Technology of China
Hefei
China