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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

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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
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > 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
Dates:
DateEvent
26 May 2017Published
19 December 2016Accepted
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
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
UNSPECIFIEDFundação de Amparo à Pesquisa do Estado de Minas Geraishttp://dx.doi.org/10.13039/501100004901
UNSPECIFIEDConselho Nacional de Desenvolvimento Científico e Tecnológicohttp://dx.doi.org/10.13039/501100003593
UNSPECIFIEDH2020 European Research Councilhttp://dx.doi.org/10.13039/100010663
UNSPECIFIEDLeverhulme Trusthttp://dx.doi.org/10.13039/501100000275
UNSPECIFIEDEngineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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