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- W2907738206 abstract "We prove that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves, are two-sided and have multiplicity one. This confirms a conjecture by Marques-Neves. We prove that in a bumpy metric each volume spectrum is realized by the min-max value of certain relative homotopy class of sweepouts of boundaries of Caccioppoli sets. The main result follows by approximating such min-max value using the min-max theory for hypersurfaces with prescribed mean curvature established by the author with Zhu." @default.
- W2907738206 created "2019-01-11" @default.
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- W2907738206 date "2019-01-04" @default.
- W2907738206 modified "2023-09-23" @default.
- W2907738206 title "On the Multiplicity One Conjecture in Min-max theory" @default.
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- W2907738206 doi "https://doi.org/10.48550/arxiv.1901.01173" @default.
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