Uniqueness of tangent cone for biharmonic map with isolated singularity

TL;DR

This paper proves the uniqueness of tangent cones for certain biharmonic maps with isolated singularities, extending Simon’s results to extrinsic biharmonic maps into compact analytic submanifolds.

Contribution

It establishes the uniqueness of tangent cones for minimizing extrinsic biharmonic maps with isolated singularities, under specific target manifold conditions.

Findings

Uniqueness of tangent cone proven for extrinsic biharmonic maps.

Results extend Simon’s classical theorem to biharmonic maps.

Applicable to maps into compact analytic submanifolds.

Abstract

In this paper, we study the problem of uniqueness of 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.