Second order rectifiability of integral varifolds of locally bounded first variation

Ulrich Menne

doi:10.1007/s12220-011-9261-5

Second order rectifiability of integral varifolds of locally bounded first variation

Ulrich Menne^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

36 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 language	English
Pages (from-to)	709-763
Number of pages	55
Journal	Journal of Geometric Analysis
Volume	23
Issue number	2
DOIs	https://doi.org/10.1007/s12220-011-9261-5
Publication status	Published - 2013 Apr
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-011-9261-5

Cite this

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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.",

keywords = "Integral varifold, Locally bounded first variation, Second fundamental form, Second order rectifiability",

author = "Ulrich Menne",

note = "Funding Information: The author acknowledges financial support via the DFG Forschergruppe 469. The major part of this work was accomplished while the author was at the University of T{\"u}bingen. Some parts were done at the ETH Z{\"u}rich and the work was put in its final form at the AEI Golm. AEI publication number AEI-2008-065.",

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PY - 2013/4

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N2 - 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.

AB - 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.

KW - Integral varifold

KW - Locally bounded first variation

KW - Second fundamental form

KW - Second order rectifiability

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Second order rectifiability of integral varifolds of locally bounded first variation

Abstract

Keywords

ASJC Scopus subject areas

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