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March 2018 Comparing the Morse index and the first Betti number of minimal hypersurfaces
Lucas Ambrozio, Alessandro Carlotto, Ben Sharp
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J. Differential Geom. 108(3): 379-410 (March 2018). DOI: 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.

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Lucas Ambrozio. Alessandro Carlotto. Ben Sharp. "Comparing the Morse index and the first Betti number of minimal hypersurfaces." J. Differential Geom. 108 (3) 379 - 410, March 2018. https://doi.org/10.4310/jdg/1519959621

Information

Received: 4 February 2016; Published: March 2018
First available in Project Euclid: 2 March 2018

zbMATH: 1385.53051
MathSciNet: MR3770846
Digital Object Identifier: 10.4310/jdg/1519959621

Rights: Copyright © 2018 Lehigh University

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Vol.108 • No. 3 • March 2018
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