论文标题
局部最大化宽度的宽度指标
Locally Maximizing Metric of Width on Manifolds with Boundary
论文作者
论文摘要
在本文中，我们使用Min-Max理论来研究具有边界$（m^{n+1}，\ partial m，g）$的紧凑型歧管中存在的自由边界最小值（FBMHS），其中$ 2 \ leq n \ leq n \ leq 6 $。假设$ g $是$ m $的合规类宽度的局部最大化器，并且所有嵌入式的FBMHS in $ m $都适当地嵌入了，我们显示了一系列嵌入了适当嵌入的等均衡分布的FBMHS的序列。这项工作扩展了Ambrozio-Montezuma的结果[2]。
In this paper we use min-max theory to study the existence free boundary minimal hypersurfaces (FBMHs) in compact manifolds with boundary $(M^{n+1}, \partial M, g)$, where $2\leq n\leq 6$. Under the assumption that $g$ is a local maximizer of the width of $M$ in its comformal class, and all embedded FBMHs in $M$ are properly embedded, we show the existence of a sequence of properly embedded equidistributed FBMHs. This work extends the result of Ambrozio-Montezuma [2].
