Second Order Rectifiability of Integral Varifolds of Locally Bounded First Variation

被引：30

作者：

Menne, Ulrich ^{[1
]}

机构：

[1] Albert Einstein Inst, Max Planck Inst Gravitat Phys, OT Golm, D-14476 Golm, Germany

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2013年 / 23卷 / 02期

关键词：

Integral varifold; Locally bounded first variation; Second order rectifiability; Second fundamental form; CURVATURE; EQUATIONS; EXISTENCE; SURFACES;

D O I：

10.1007/s12220-011-9261-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that every integral varifold in an open subset of Euclidean space whose first variation with respect to area is representable by integration can be covered by a countable collection of submanifolds of the same dimension of class 2 and that their mean curvature agrees almost everywhere with the variationally defined generalized mean curvature of the varifold.

引用

页码：709 / 763

页数：55

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