On the Compactness Theorem for Embedded Minimal Surfaces in 3-manifolds with Locally Bounded Area and Genus
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arXiv
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| Format: | Preprint |
| Published: |
2015
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| _version_ | 1866910306915057664 |
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| author | White, Brian |
| author_facet | White, Brian |
| contents | Given a sequence of properly embedded minimal surfaces in a $3$-manifold with local bounds on area and genus, we prove subsequential convergence, smooth away from a discrete set, to a smooth embedded limit surface, possibly with multiplicity, and we analyze what happens when one blows up the surfaces near a point where the convergence is not smooth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1503_02190 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | On the Compactness Theorem for Embedded Minimal Surfaces in 3-manifolds with Locally Bounded Area and Genus White, Brian Differential Geometry 53A10 (primary), and 49Q05 (secondary) Given a sequence of properly embedded minimal surfaces in a $3$-manifold with local bounds on area and genus, we prove subsequential convergence, smooth away from a discrete set, to a smooth embedded limit surface, possibly with multiplicity, and we analyze what happens when one blows up the surfaces near a point where the convergence is not smooth. |
| title | On the Compactness Theorem for Embedded Minimal Surfaces in 3-manifolds with Locally Bounded Area and Genus |
| topic | Differential Geometry 53A10 (primary), and 49Q05 (secondary) |
| url | https://arxiv.org/abs/1503.02190 |