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Research Talk – Xin Zhou, University of California, Santa Barbara

February 19 @ 11:00 am - 12:00 pm

Title: 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 as the key step to establish a Morse theory for the area functional. 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. The talk will be for general audience.


February 19
11:00 am - 12:00 pm


David Cruz-Uribe
dcruzuribe at ua.edu