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Smooth compactness of f-minimal hypersurfaces with bounded f-index
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Barbosa, Ezequiel Rodrigues, Sharp, Benjamin G. and Wei, Yong (2017) Smooth compactness of f-minimal hypersurfaces with bounded f-index. Proceedings of the American Mathematical Society, 145 . 4945-4961 . doi:10.1090/proc/13628
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Official URL: https://doi.org/10.1090/proc/13628
Abstract
Let $ (M^{n+1},g,e^{-f}d\mu )$ be a complete smooth metric measure space with $ 2\leq n\leq 6$ and Bakry-Émery Ricci curvature bounded below by a positive constant. We prove a smooth compactness theorem for the space of complete embedded $ f$-minimal hypersurfaces in $ M$ with uniform upper bounds on $ f$-index and weighted volume. As a corollary, we obtain a smooth compactness theorem for the space of embedded self-shrinkers in $ \mathbb{R}^{n+1}$ with $ 2\leq n\leq 6$. We also prove some estimates on the $ f$-index of $ f$-minimal hypersurfaces
| Item Type: | Journal Article | ||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||||||||
| Divisions: | Faculty of Science > Mathematics | ||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Hypersurfaces, Metric spaces | ||||||||||||||||||
| Journal or Publication Title: | Proceedings of the American Mathematical Society | ||||||||||||||||||
| Publisher: | American Mathematical Society | ||||||||||||||||||
| ISSN: | 0002-9939 | ||||||||||||||||||
| Official Date: | 26 May 2017 | ||||||||||||||||||
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| Volume: | 145 | ||||||||||||||||||
| Page Range: | 4945-4961 | ||||||||||||||||||
| DOI: | 10.1090/proc/13628 | ||||||||||||||||||
| Status: | Peer Reviewed | ||||||||||||||||||
| Publication Status: | Published | ||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||
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