Ambrozio, L, Carlotto, A and Sharp, B orcid.org/0000-0002-7238-4993 (2018) Comparing the Morse index and the first Betti number of minimal hypersurfaces. Journal of Differential Geometry, 108 (3). pp. 379-410. ISSN 0022-040X
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 27 Jun 2018 09:45 |
Last Modified: | 31 Jan 2019 14:42 |
Status: | Published |
Publisher: | International Press |
Identification Number: | 10.4310/jdg/1519959621 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:132568 |