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  Weakly differentiable functions on varifolds

Menne, U. (2016). Weakly differentiable functions on varifolds. Indiana University Mathematics Journal, 65(3), 977-1088. doi:10.1512/iumj.2016.65.5829.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0024-4269-7 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-F76D-E
Genre: Journal Article

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 Creators:
Menne, Ulrich1, Author              
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1Geometric Measure Theory, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_1753352              

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Free keywords: Mathematics, Differential Geometry, math.DG,Mathematics, Classical Analysis and ODEs, math.CA,
 Abstract: The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration by parts identities for certain compositions with smooth functions. In this class the idea of zero boundary values is realised using the relative perimeter of superlevel sets. Results include a variety of Sobolev Poincar\'e type embeddings, embeddings into spaces of continuous and sometimes H\"older continuous functions, pointwise differentiability results both of approximate and integral type as well as coarea formulae. As prerequisite for this study decomposition properties of such varifolds and a relative isoperimetric inequality are established. Both involve a concept of distributional boundary of a set introduced for this purpose. As applications the finiteness of the geodesic distance associated to varifolds with suitable summability of the mean curvature and a characterisation of curvature varifolds are obtained.

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 Dates: 2014-11-122014201520162016
 Publication Status: Published in print
 Pages: 84
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1411.3287
URI: http://arxiv.org/abs/1411.3287
DOI: 10.1512/iumj.2016.65.5829
 Degree: -

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Title: Indiana University Mathematics Journal
Source Genre: Journal
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Publ. Info: Bloomington, Ind. : Dept. of Mathematics, Indiana University
Pages: - Volume / Issue: 65 (3) Sequence Number: - Start / End Page: 977 - 1088 Identifier: ISSN: 0022-2518
CoNE: /journals/resource/991042730666442