Diff. Geom, Math. Phys., PDE Seminar: Xin Zhou

  • Date: 04/04/2019
  • Time: 15:30
Xin Zhou, UC Santa Barbara

University of British Columbia


Multiplicity One Conjecture in Min-max theory


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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Location: MATH 225