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Differential Geometry Seminar - Xin Zhou

Xin Zhou
February 28, 2019
2:30PM - 3:30PM
Journalism Building 221

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Add to Calendar 2019-02-28 14:30:00 2019-02-28 15:30:00 Differential Geometry Seminar - Xin Zhou Title: Multiplicity One Conjecture in Min-max theory Speaker: Xin Zhou (University of California Santa Barbara and Institute for Advanced Study) Abstract: I will present a recent proof of the Multiplicity One Conjecture in Min-max theory. This conjecture was raised by Marques and Neves. It says 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 all two-sided and have multiplicity one. As direct corollaries, it implies the generalized Yau's conjecture for such manifolds with positive Ricci curvature, which says that there exist a sequence of minimal hypersurfaces with area tending to infinity, and the Weighted Morse Index Bound Conjecture by Marques and Neves. Journalism Building 221 Department of Mathematics math@osu.edu America/New_York public

Title: Multiplicity One Conjecture in Min-max theory

SpeakerXin Zhou (University of California Santa Barbara and Institute for Advanced Study)

Abstract: I will present a recent proof of the Multiplicity One Conjecture in Min-max theory. This conjecture was raised by Marques and Neves. It says 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 all two-sided and have multiplicity one. As direct corollaries, it implies the generalized Yau's conjecture for such manifolds with positive Ricci curvature, which says that there exist a sequence of minimal hypersurfaces with area tending to infinity, and the Weighted Morse Index Bound Conjecture by Marques and Neves.

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