Multiplicity One Conjecture in Minmax theory
Multiplicity One Conjecture in Minmax theory

Xin Zhou, University of California Santa Barbara and IAS
Fine Hall 314
I will present a recent proof of the Multiplicity One Conjecture in Minmax 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 minmax minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, MarquesNeves are all twosided 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 nonisometric minimal hypersurfaces, and the Weighted Morse Index Bound Conjecture by Marques and Neves.