Second order rectifiability of integral varifolds of locally bounded first variation
Differential Geometry
2013-03-04 v3 Analysis of PDEs
Abstract
In this work it is shown that every integral varifold in an open subset of Euclidian space of locally bounded first variation can be covered by a countable collection of submanifolds of class C^2. Moreover, the mean curvature of each member of the collection agrees with the mean curvature of the varifold almost everywhere with respect to the varifold.
Cite
@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}
}
Comments
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