An Epiperimetric Inequality Related to the Analyticity of Minimal Surfaces
An Epiperimetric Inequality Related to the Analyticity of Minimal Surfaces
复制标题
与最小曲面解析性相关的周长不等式
DOI：
10.2307/1970488
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发表时间：
1964
影响因子：
4.9
通讯作者：
E. Reifenberg
中科院分区：
文献类型：
--
作者：
E. Reifenberg
本文的目的是使我们能够证明，一个极小曲面是解析的点，其密度是1。这将在其他地方[1]进行，但该研究的主要关键是我们在这里证明的以下结果：假设Y是R中维数为m的可定向多面体锥，顶点为0，其边界位于中心为0的单位球面上。然后，如果Y足够靠近直径平面，我们可以构造一个具有相同边界的新曲面Y*，使得
The purpose of this paper is to enable us to prove that a minimal surface is analytic at points where its density is one. This will be done elsewhere [1], but the main key to that investigation is the following result which we prove here: Suppose Y is an orientable polyhedral cone, with vertex 0, of dimension m in R., whose boundary lies on the unit sphere with center 0. Then, if Y lies sufficiently near to a diametral plane, we can construct a new surface Y* with the same boundary such that