Smooth compactness of f-minimal hypersurfaces with bounded f-index

Ezequiel Barbosa; Ben Sharp; Yong Wei

doi:10.1090/proc/13628

Smooth compactness of f-minimal hypersurfaces with bounded f-index

Ezequiel Barbosa, Ben Sharp, Yong Wei

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Let (Mⁿ⁺¹, g, e^−f dμ) be a complete smooth metric measure space with 2 ≤ n ≤ 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 ℝⁿ⁺¹ with 2 ≤ n ≤ 6. We also prove some estimates on the f-index of f-minimal hypersurfaces.

Original language	English
Pages (from-to)	4945-4961
Number of pages	17
Journal	Proceedings of the American Mathematical Society
Volume	145
Issue number	11
DOIs	https://doi.org/10.1090/proc/13628
Publication status	Published - 2017

Access to Document

10.1090/proc/13628

Cite this

@article{403fb319ca7742878c42e571743b2805,

title = "Smooth compactness of f-minimal hypersurfaces with bounded f-index",

abstract = "Let (Mn+1, g, e−f dμ) be a complete smooth metric measure space with 2 ≤ n ≤ 6 and Bakry-{\'E}mery 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 ℝn+1 with 2 ≤ n ≤ 6. We also prove some estimates on the f-index of f-minimal hypersurfaces.",

author = "Ezequiel Barbosa and Ben Sharp and Yong Wei",

note = "Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",

year = "2017",

doi = "10.1090/proc/13628",

language = "English",

volume = "145",

pages = "4945--4961",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "11",

}

TY - JOUR

T1 - Smooth compactness of f-minimal hypersurfaces with bounded f-index

AU - Barbosa, Ezequiel

AU - Sharp, Ben

AU - Wei, Yong

PY - 2017

Y1 - 2017

N2 - Let (Mn+1, g, e−f dμ) be a complete smooth metric measure space with 2 ≤ n ≤ 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 ℝn+1 with 2 ≤ n ≤ 6. We also prove some estimates on the f-index of f-minimal hypersurfaces.

AB - Let (Mn+1, g, e−f dμ) be a complete smooth metric measure space with 2 ≤ n ≤ 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 ℝn+1 with 2 ≤ n ≤ 6. We also prove some estimates on the f-index of f-minimal hypersurfaces.

UR - https://www.scopus.com/pages/publications/85029604074

U2 - 10.1090/proc/13628

DO - 10.1090/proc/13628

M3 - Article

SN - 0002-9939

VL - 145

SP - 4945

EP - 4961

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

Smooth compactness of f-minimal hypersurfaces with bounded f-index

Abstract

Access to Document

Other files and links

Fingerprint

Cite this