Topology of surfaces with finite Willmore energy

Jie Zhou

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arXiv · 1912.07014

Topology of surfaces with finite Willmore energy

Jie Zhou

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Abstract

In this paper, we study the critical case of the Allard regularity theorem. Combining with Reifenberg's topological disk theorem, we get a critical Allard-Reifenberg type regularity theorem. As a main result, we get the topological finiteness for a class of properly immersed surfaces in $\mathbb{R}^n$ with finite Willmore energy. Especially, we prove a removability of singularity of multiplicity one surface with finite Willmore energy and a uniqueness theorem of the catenoid under no a priori topological finiteness assumption.

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Jie Zhou. 2019-12-15. Topology of surfaces with finite Willmore energy. https://arxiv.org/abs/1912.07014

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