Compactness and existence results for free boundary minimal hypersurfaces

Abstract: A hypersurface in a compact manifold $M$ with boundary is called a free boundary minimal hypersurface (FBMH) if it is minimal and meets the boundary of $M$ orthogonally. Such hypersurfaces arise naturally as critical points of the area functional in $M$. If we do not assume any boundary convexity of $M$, then the FBMH may be improper, i.e., the interior of the FBMH may touch $/partial M$. We will discuss the compactness and existence results for FBMHs in this general setting.

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Contact person: Professor SHENG Weimin (shengweimin@zju.edu.cn)