论文标题
多重性一个用于最小的最大理论，具有边界及其应用的紧凑型歧管
Multiplicity one for min-max theory in compact manifolds with boundary and its applications
论文作者
论文摘要
我们证明，在紧凑的歧管中，最小值的最小边界的多重性一个定理，对于通用指标，尺寸为3至7之间的边界。为了解决这个问题，我们使用规定的平均曲率开发了自由边界超表面的存在和规律性理论，其中包括最小化的规律性理论，紧凑型理论和具有莫尔斯索引界限的通用最小值理论。作为应用，我们在欧几里得空间中的单位球和平均曲率流动的自我缩短器中构建了新的自由边界最小的超曲面，并构建了自弯曲的平均曲率流动器。
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.
