论文标题
最小最小的高度曲面和障碍物
Min-max Minimal Hypersurfaces with Obstacle
论文作者
论文摘要
我们研究了在限制边界平滑歧管的高空曲面之间面积功能的最小最大理论。对于满足变异不平等的整体varifolds，证明了Schoen-Simon类型的规律性结果，并限制在内部稳定的最小超表面。基于此，我们表明，对于任何可接受的扫描家庭中的$π$，在与边界紧凑的歧管中均存在一个封闭的$ c^{1,1,1} $ hypersurface，带有codimension $ \ geq 7 $ singular setular in e Intereror中的单数，并且具有平均值的曲率，并沿边界向外指向width $ \ textbfff {l textbf {l} $ fornouse of Bounce of toarnder。
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 $C^{1,1}$ hypersurface with codimension$\geq 7$ singular set in the interior and having mean curvature pointing outward along boundary realizing the width $\textbf{L}(Π)$.
