The concept of varifold
Differential Geometry
2017-10-23 v4 Analysis of PDEs
Classical Analysis and ODEs
Abstract
We survey - by means of 20 examples - the concept of varifold, as generalised submanifold, with emphasis on regularity of integral varifolds with mean curvature, while keeping prerequisites to a minimum. Integral varifolds are the natural language for studying the variational theory of the area integrand if one considers, for instance, existence or regularity of stationary (or, stable) surfaces of dimension at least three, or the limiting behaviour of sequences of smooth submanifolds under area and mean curvature bounds.
Keywords
Cite
@article{arxiv.1705.05253,
title = {The concept of varifold},
author = {Ulrich Menne},
journal= {arXiv preprint arXiv:1705.05253},
year = {2017}
}
Comments
The present text is a version with additional references but without figures of a note compiled for the Notices of the American Mathematical Society. (v4: considerably expanded introduction, 6 pages)