Second order rectifiability of integral varifolds of locally bounded first variation

Ulrich Menne*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)709-763
Number of pages55
JournalJournal of Geometric Analysis
Volume23
Issue number2
DOIs
Publication statusPublished - 2013 Apr
Externally publishedYes

Keywords

  • Integral varifold
  • Locally bounded first variation
  • Second fundamental form
  • Second order rectifiability

ASJC Scopus subject areas

  • Geometry and Topology

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