English

Compactness and Rigidity of $\lambda$-Surfaces

Differential Geometry 2018-12-07 v2

Abstract

In this paper we develop the compactness theorem for λ\lambda-surface in R3\mathbb R^3 with uniform λ\lambda, genus, and area growth. This theorem can be viewed as a generalization of Colding-Minicozzi's compactness theorem for self-shrinkers in R3\mathbb R^3. As an application of this compactness theorem, we prove a rigidity theorem for convex λ\lambda-surfaces.

Keywords

Cite

@article{arxiv.1804.09316,
  title  = {Compactness and Rigidity of $\lambda$-Surfaces},
  author = {Ao Sun},
  journal= {arXiv preprint arXiv:1804.09316},
  year   = {2018}
}

Comments

19 pages. Correct a mistake pointing out by Jonathan Zhu. Comments are welcomed!

R2 v1 2026-06-23T01:34:45.522Z