报告人：周鑫（加州大学和普林斯顿高等研究中心）

时 间：2019-05-13   15:00-16:00

地 点：Room 1114, Sciences Building No. 1

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 areas tending to infinity, and the Weighted Morse Index Bound Conjecture by Marques and Neves.