Asymptotic Analysis of embedded Willmore spheres in 3-dimensional manifolds

Chih-Kang Huang

Asymptotic Analysis of embedded Willmore spheres in 3-dimensional manifolds

Analysis of PDEs 2017-11-02 v2 Differential Geometry

Authors: Chih-Kang Huang

Abstract

In this paper, we show that, under arbitrary bounded Willmore energy assumption, embedded Willmore spheres (or more generally, embedded Willmore spheres under area constraint) with small diameter in a given $3$ -dimensional Riemannian manifold $(M, h)$ necessarily concentrate at a critical point of the scalar curvature of $(M, h)$ . This generalizes the result obtained by Laurain and Mondino for embedded Willmore spheres of small energy.

Keywords

embedded Willmore spheres Riemannian manifold scalar curvature asymptotic analysis concentration critical point area constraint

Cite

@article{arxiv.1710.08732,
  title  = {Asymptotic Analysis of embedded Willmore spheres in 3-dimensional manifolds},
  author = {Chih-Kang Huang},
  journal= {arXiv preprint arXiv:1710.08732},
  year   = {2017}
}

Comments

The Theorem 9 in Section 3 of the paper has recently been found by author to be completely wrong. The rest of the results (including the goal of the paper) is then inappropriate and therefore needs to be entirely rewritten

Asymptotic Analysis of embedded Willmore spheres in 3-dimensional manifolds

Abstract

Keywords

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