论文标题
自由边界最小表面的规律性在本地多面体结构域中
Regularity of free boundary minimal surfaces in locally polyhedral domains
论文作者
论文摘要
我们证明了在Lipschitz域中自由晶体最小表面的Allard型规则定理，该域在凸Polyhedra上本地建模。我们表明，如果这样的最小表面足够靠近适当的自由边缘平面，则表面为$ c^{1，α} $在该平面上。我们应用定理来证明自由边界的局部规律性结果，以最大程度地减少曲面和相对等级区域。
We prove an Allard-type regularity theorem for free-boundary minimal surfaces in Lipschitz domains locally modelled on convex polyhedra. We show that if such a minimal surface is sufficiently close to an appropriate free-boundary plane, then the surface is $C^{1,α}$ graphical over this plane. We apply our theorem to prove partial regularity results for free-boundary minimizing hypersurfaces, and relative isoperimetric regions.
