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Multiplicity One for Min-max Theory in Compact Manifolds with Boundary and Its Applications by Sun, Ao; Wang, Zhichao; Zhou, Xin is a scholarly article available to read on EtoBox.

What is Multiplicity One for Min-max Theory in Compact Manifolds with Boundary and Its Applications about?

We prove 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 develop existence and regularity theory for free boundary hypersurface with prescribed mean curvature, which includes the regularity theory for minimizers, compactness theory, and a generic min-max theory with Morse index bounds. As applications, we construct new free boundary minimal hypersurfaces in the unit balls in Euclidean spaces and self-shrinkers of the mean curvature flows with arbitrarily large entropy.

Author

Sun, Ao; Wang, Zhichao; Zhou, Xin

Published

2020

Language

EN