Limiting behavior of sequences of properly embedded minimal disks
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2017
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| _version_ | 1866929222407159808 |
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| author | Hoffman, David White, Brian |
| author_facet | Hoffman, David White, Brian |
| contents | We develop a theory of "minimal $θ$-graphs" and characterize the behavior of limit laminations of such surfaces, including an understanding of their limit leaves and their curvature blow-up sets. We use this to prove that it is possible to realize families of catenoids in euclidean space as limit leaves of sequences of embedded minimal disks, even when there is no curvature blow-up. Our methods work in a more general Riemannian setting, including hyperbolic space. This allows us to establish the existence of a complete, simply connected, minimal surface in hyperbolic space that is not properly embedded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1706_06186 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Limiting behavior of sequences of properly embedded minimal disks Hoffman, David White, Brian Differential Geometry 53A10 (Primary), 49Q05, 53C42 (Secondary) We develop a theory of "minimal $θ$-graphs" and characterize the behavior of limit laminations of such surfaces, including an understanding of their limit leaves and their curvature blow-up sets. We use this to prove that it is possible to realize families of catenoids in euclidean space as limit leaves of sequences of embedded minimal disks, even when there is no curvature blow-up. Our methods work in a more general Riemannian setting, including hyperbolic space. This allows us to establish the existence of a complete, simply connected, minimal surface in hyperbolic space that is not properly embedded. |
| title | Limiting behavior of sequences of properly embedded minimal disks |
| topic | Differential Geometry 53A10 (Primary), 49Q05, 53C42 (Secondary) |
| url | https://arxiv.org/abs/1706.06186 |