局部有界一阶变差的积分varifold的二阶可求积性
微分几何
2013-03-04 v3 偏微分方程分析
摘要
本文证明了欧几里得空间开子集中每个具有局部有界一阶变差的积分varifold可以被一个可数族C^2类子流形所覆盖。此外，该族中每个成员的平均曲率在varifold的几乎处处意义下与varifold的平均曲率一致。
关键词
引用
@article{arxiv.0808.3665,
title = {Second order rectifiability of integral varifolds of locally bounded first variation},
author = {Ulrich Menne},
journal= {arXiv preprint arXiv:0808.3665},
year = {2013}
}
备注
v1: 34 pages, no figures; v2: revised presentation, material of 0909.3253 and 0808.3665 reorganised, parts moved to 0909.3253v2, parts from 0909.3253v1 included, this version now depends on 0909.3253v2, comparison to Hutchinson's second fundamental form added, 40 pages, no figures; v3: introduction and 4.5 revised, 3.8 and one reference added, one reference updated, 40 pages, no figures