2020/10/26 by Zhihan Wang, Wang, Zhihan
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #math.DG
paper · pdf · doi:10.48550/arxiv.2010.13305
23 pages
arxiv created 2020/10/26 · openalex publication_date 2020/10/26 · arxiv updated 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study min-max theory for area functional among hypersurfaces constrained in a smooth manifold with boundary. A Schoen-Simon-type regularity result is proved for integral varifolds which satisfy a variational inequality and restrict to a stable minimal hypersurface in the interior. Based on this, we show that for any admissible family of sweepouts Π in a compact manifold with boundary, there always exists a closed C1,1 hypersurface with codimension≥ 7 singular set in the interior and having mean curvature pointing outward along boundary realizing the width L(Π).