Mean convex mean curvature flow with free boundary
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866912453848203264 |
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| author | Edelen, Nick Haslhofer, Robert Ivaki, Mohammad N. Zhu, Jonathan J. |
| author_facet | Edelen, Nick Haslhofer, Robert Ivaki, Mohammad N. Zhu, Jonathan J. |
| contents | In this paper, we generalize White's regularity and structure theory for mean-convex mean curvature flow to the setting with free boundary. A major new challenge in the free boundary setting is to derive an a priori bound for the ratio between the norm of the second fundamental form and the mean curvature. We establish such a bound via the maximum principle for a triple-approximation scheme, which combines ideas from Edelen, Haslhofer-Hershkovits, and Volkmann. Other important new ingredients are a Bernstein-type theorem and a sheeting theorem for low entropy free boundary flows in a halfslab, which allow us to rule out multiplicity 2 (half-)planes as possible tangent flows and, for mean convex domains, as possible limit flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_01186 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Mean convex mean curvature flow with free boundary Edelen, Nick Haslhofer, Robert Ivaki, Mohammad N. Zhu, Jonathan J. Differential Geometry Analysis of PDEs In this paper, we generalize White's regularity and structure theory for mean-convex mean curvature flow to the setting with free boundary. A major new challenge in the free boundary setting is to derive an a priori bound for the ratio between the norm of the second fundamental form and the mean curvature. We establish such a bound via the maximum principle for a triple-approximation scheme, which combines ideas from Edelen, Haslhofer-Hershkovits, and Volkmann. Other important new ingredients are a Bernstein-type theorem and a sheeting theorem for low entropy free boundary flows in a halfslab, which allow us to rule out multiplicity 2 (half-)planes as possible tangent flows and, for mean convex domains, as possible limit flows. |
| title | Mean convex mean curvature flow with free boundary |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/1911.01186 |