Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Index estimates for free boundary minimal hypersurfaces

Tools
- Tools
+ Tools

Ambrozio, Lucas, Carlotto, Alessandro and Sharp, Benjamin G. (2018) Index estimates for free boundary minimal hypersurfaces. Mathematische Annalen, 370 (3-4). pp. 1063-1078. doi:10.1007/s00208-017-1549-8 ISSN 0025-5831.

[img]
Preview
PDF
WRAP-index-estimates-free-boundary-hypersurfaces-Sharp-2017.pdf - Accepted Version - Requires a PDF viewer.

Download (489Kb) | Preview
Official URL: https://doi.org/10.1007/s00208-017-1549-8

Request Changes to record.

Abstract

We show that the Morse index of a properly embedded free boundary minimal hypersurface in a strictly mean convex domain of the Euclidean space grows linearly with the dimension of its first relative homology group (which is at least as big as the number of its boundary components, minus one). In ambient dimension three, this implies a lower bound for the index of a free boundary minimal surface which is linear both with respect to the genus and the number of boundary components. Thereby, the compactness theorem by Fraser and Li implies a strong compactness theorem for the space of free boundary minimal surfaces with uniformly bounded Morse index inside a convex domain. Our estimates also imply that the examples constructed, in the unit ball, by Fraser-Schoen and Folha-Pacard Zolotareva have arbitrarily large index. Extensions of our results to more general settings (including various classes of positively curved Riemannian manifolds and other convexity assumptions) are discussed

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, Riemannian manifolds
Journal or Publication Title: Mathematische Annalen
Publisher: Springer Verlag
ISSN: 0025-5831
Official Date: April 2018
Dates:
DateEvent
April 2018Published
4 May 2017Available
26 April 2017Accepted
Volume: 370
Number: 3-4
Page Range: pp. 1063-1078
DOI: 10.1007/s00208-017-1549-8
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 19 July 2017
Date of first compliant Open Access: 4 May 2018
Funder: European Research Council (ERC), Scuola normale superiore (Italy)
Grant number: Start Grant PSC and LMCF 278940

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us