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arXiv · 2108.06052

No breather theorems for the mean curvature flow

Liang Cheng·Yongjia Zhang
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Abstract

In this article we study the breathers of the mean curvature flow in the Euclidean space. A breather is a solution to the mean curvature flow which repeats itself up to isometry and scaling once in a while. We prove several no breather theorems in the noncompact category, that is, under certain conditions, a breather of the mean curvature flow must be a solitonic solution (self-shrinker, self-expander, or translator).

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Liang Cheng, Yongjia Zhang. 2021-08-13. No breather theorems for the mean curvature flow. https://arxiv.org/abs/2108.06052

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