A strong stability condition on minimal submanifolds and its implications
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 dynamical stability theorem of the mean curvature flow for minimal submanifolds that satisfy this condition. The latter theo...
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| Published in | Journal für die reine und angewandte Mathematik Vol. 2020; no. 764; pp. 111 - 156 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
De Gruyter
01.07.2020
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| Online Access | Get full text |
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| Summary: | 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
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
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 [
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which applies only to calibrated submanifolds of special holonomy ambient manifolds. |
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| ISSN: | 0075-4102 1435-5345 |
| DOI: | 10.1515/crelle-2018-0038 |