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arXiv · 1804.09316

Compactness and Rigidity of $\lambda$-Surfaces

Ao Sun
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Abstract

In this paper we develop the compactness theorem for $\lambda$-surface in $\mathbb R^3$ with uniform $\lambda$, genus, and area growth. This theorem can be viewed as a generalization of Colding-Minicozzi's compactness theorem for self-shrinkers in $\mathbb R^3$. As an application of this compactness theorem, we prove a rigidity theorem for convex $\lambda$-surfaces.

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Ao Sun. 2018-04-25. Compactness and Rigidity of $\lambda$-Surfaces. https://arxiv.org/abs/1804.09316

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