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A strong stability condition on minimal submanifolds and its implications
Journal für die reine und angewandte Mathematik ( IF 1.2 ) Pub Date : 2019-01-22 , DOI: 10.1515/crelle-2018-0038
Chung-Jun Tsai, Mu-Tao Wang

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 𝒞1 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 𝒞1 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 [] which applies only to calibrated submanifolds of special holonomy ambient manifolds.

中文翻译:

最小子流形上的强稳定性条件及其含义

我们确定了最小子流形上的强稳定性条件,这暗示了唯一性和动态稳定性。特别是,我们证明了唯一性定理和𝒞1个满足此条件的最小子流形的平均曲率流的动力稳定性定理。后一个定理指出,一个子流形中任何其他子流形的平均曲率流。𝒞1个这种最小子流形的邻域一直存在,并且以指数形式收敛到最小子流形。这扩展了我们先前的唯一性和稳定性定理[],该定理仅适用于特殊完整环境歧管的校准子流形。
更新日期:2019-01-22
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