Non-fattening of mean curvature flow at singularities of mean convex type
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866917573256282112 |
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| author | Hershkovits, Or White, Brian |
| author_facet | Hershkovits, Or White, Brian |
| contents | We show that a mean curvature flow starting from a compact, smoothly embedded hypersurface M remains unique past singularities, provided the singularities are of mean convex type, i.e., if around each singular point, the surface moves in one direction. Specifically, the level set flow of M does not fatten if all singularities are of mean convex type. This generalizes the well known fact that the level set flow of a mean convex initial hypersurface M does not fatten. This also provides the first instance where non-fattening is concluded from local information around the singular set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1704_00431 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Non-fattening of mean curvature flow at singularities of mean convex type Hershkovits, Or White, Brian Differential Geometry 53C44 (Primary), 49Q20 (Secondary) We show that a mean curvature flow starting from a compact, smoothly embedded hypersurface M remains unique past singularities, provided the singularities are of mean convex type, i.e., if around each singular point, the surface moves in one direction. Specifically, the level set flow of M does not fatten if all singularities are of mean convex type. This generalizes the well known fact that the level set flow of a mean convex initial hypersurface M does not fatten. This also provides the first instance where non-fattening is concluded from local information around the singular set. |
| title | Non-fattening of mean curvature flow at singularities of mean convex type |
| topic | Differential Geometry 53C44 (Primary), 49Q20 (Secondary) |
| url | https://arxiv.org/abs/1704.00431 |