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arXiv · 1710.00433

A strong stability condition on minimal submanifolds and its implications

Chung-Jun Tsai·Mu-Tao Wang
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Abstract

We identify a strong stability condition on minimal submanifolds that implies uniqueness and dynamical stability properties. In particular, we prove a uniqueness theorem and a C^1 dynamical stability theorem of the mean curvature flow for minimal submanifolds that satisfy this condition. The latter theorem states that the mean curvature flow of any other submanifold in a C^1 neighborhood of such a minimal submanifold exists for all time, and converges exponentially to the minimal one. This extends our previous uniqueness and stability theorem [arXiv:1605.03645] which applies only to calibrated submanifolds of special holonomy ambient manifolds.

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Chung-Jun Tsai, Mu-Tao Wang. 2017-10-01. A strong stability condition on minimal submanifolds and its implications. https://arxiv.org/abs/1710.00433

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