Department of Mathematics,
University of California San Diego
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Math 258 - Differential Geometry
Xin Zhou
UCSB
Multiplicity One Conjecture in Min-max theory
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 infinitely many pairwise non-isometric minimal hypersurfaces, and the Weighted Morse Index Bound Conjecture by Marques and Neves.
Host: Lei Ni
January 16, 2019
1:00 PM
AP&M 5829
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