Multiplicity one for min-max theory in compact manifolds with boundary and its applications

Abstract: In this talk, we introduce the multiplicity one theorem for min-max free boundary minimal hypersurfaces in compact manifolds with boundary of dimension between 3 and 7 for generic metrics. To approach this, we developed the min-max theory for free boundary h-hypersurfaces and proved the generic properness for free boundary minimal hypersurfaces. The application includes the construction of new free boundary minimal hypersurfaces in the unit balls in Euclidean spaces and self-shrinkers of the mean curvature flow with arbitrarily large entropy. This is a joint work with A. Sun and X. Zhou.

algebraic topologydifferential geometrygeometric topologymetric geometry

Audience: researchers in the topic

Comments: Zoom link: utoronto.zoom.us/j/84117185836

University of Toronto Geometry & Topology seminar