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Equidistribution of minimal hypersurfaces for generic metrics

Marques, Fernando C. and Neves, André and Song, Antoine (2019) Equidistribution of minimal hypersurfaces for generic metrics. Inventiones Mathematicae, 216 (2). pp. 421-443. ISSN 0020-9910. doi:10.1007/s00222-018-00850-5.

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For almost all Riemannian metrics (in the C∞ Baire sense) on a closed manifold Mⁿ⁺¹, 3 ≤ (n+1) ≤ 7, we prove that there is a sequence of closed, smooth, embedded, connected minimal hypersurfaces that is equidistributed in M. This gives a quantitative version of the main result of Irie et al. (Ann Math 187(3):963–972, 2018), that established density of minimal hypersurfaces for generic metrics. As in Irie et al. (2018), the main tool is the Weyl Law for the Volume Spectrum proven by Liokumovich et al. (Ann Math 187(3):933–961, 2018).

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Additional Information:The first author is partly supported by NSF-DMS-1509027 and NSF DMS-1311795. The second author is partly supported by NSF DMS-1710846 and EPSRC Programme Grant EP/K00865X/1. The third author is supported by NSF-DMS-1509027.
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Engineering and Physical Sciences Research Council (EPSRC)EP/K00865X/1
Issue or Number:2
Record Number:CaltechAUTHORS:20221026-539148000.11
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117598
Deposited By: George Porter
Deposited On:28 Oct 2022 15:36
Last Modified:28 Oct 2022 15:36

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