https://neckpinch.com/authors/xin-zhou/New arXiv papers by Xin Zhou, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2011.04136/arxiv:2011.04136Mon, 09 Nov 2020 00:00:00 GMTAo Sun, Zhichao Wang, Xin Zhou — 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.Mean curvature flowSelf-shrinkers & translatorsLimit spaces & RCDBoundaries & non-compactFree boundary & capillaryMinimal & CMC surfaces