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Comparing the Morse index and the first Betti number of minimal hypersurfaces
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Ambrozio, Lucas, Carlotto, Alessandro and Sharp, Benjamin G. (2018) Comparing the Morse index and the first Betti number of minimal hypersurfaces. Journal of Differential Geometry, 108 (3). pp. 379-410. doi:10.4310/jdg/1519959621 ISSN 0022-040X.
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Official URL: http://dx.doi.org/10.4310/jdg/1519959621
Abstract
By extending and generalizing previous work by Ros and Savo, we describe a method to show that in certain positively curved ambient manifolds the Morse index of every closed minimal hypersurface is bounded from below by a linear function of its first Betti number. The technique is flexible enough to prove that such a relation between the index and the topology of minimal hypersurfaces holds, for example, on all compact rank one symmetric spaces, on products of the circle with spheres of arbitrary dimension and on suitably pinched submanifolds of the Euclidean spaces. These results confirm a general conjecture due to Schoen and Marques–Neves for a wide class of ambient spaces.
Item Type: | Journal Article | ||||||||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Hypersurfaces, Manifolds (Mathematics), Index theory (Mathematics), Riemannian manifolds | ||||||||||||||||||
Journal or Publication Title: | Journal of Differential Geometry | ||||||||||||||||||
Publisher: | Lehigh University | ||||||||||||||||||
ISSN: | 0022-040X | ||||||||||||||||||
Official Date: | 2 March 2018 | ||||||||||||||||||
Dates: |
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Volume: | 108 | ||||||||||||||||||
Number: | 3 | ||||||||||||||||||
Page Range: | pp. 379-410 | ||||||||||||||||||
DOI: | 10.4310/jdg/1519959621 | ||||||||||||||||||
Status: | Peer Reviewed | ||||||||||||||||||
Publication Status: | Published | ||||||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||
Copyright Holders: | International Press | ||||||||||||||||||
Date of first compliant deposit: | 30 October 2019 | ||||||||||||||||||
Date of first compliant Open Access: | 30 October 2019 | ||||||||||||||||||
RIOXX Funder/Project Grant: |
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