Some applications of the isoperimetric inequality for integral varifolds

Ulrich Menne

doi:10.1515/ACV.2009.010

Some applications of the isoperimetric inequality for integral varifolds

Ulrich Menne^*

^*Corresponding author for this work

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

13 Citations (Scopus)

Abstract

In this work the isoperimetric inequality for integral varifolds of locally bounded first variation is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calderón's and Zygmund's theory of first order differentiability for functions in Lebesgue spaces from Lebesgue measure to integral varifolds.

Original language	English
Pages (from-to)	247-269
Number of pages	23
Journal	Advances in Calculus of Variations
Volume	2
Issue number	3
DOIs	https://doi.org/10.1515/ACV.2009.010
Publication status	Published - 2009 Jul
Externally published	Yes

Keywords

Height-excess
Integral varifolds
Locally bounded first variation
Tilt-excess

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1515/ACV.2009.010

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abstract = "In this work the isoperimetric inequality for integral varifolds of locally bounded first variation is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calder{\'o}n's and Zygmund's theory of first order differentiability for functions in Lebesgue spaces from Lebesgue measure to integral varifolds.",

keywords = "Height-excess, Integral varifolds, Locally bounded first variation, Tilt-excess",

author = "Ulrich Menne",

note = "Funding Information: The author acknowledges financial support via the DFG Forschergruppe 469. The research was carried out at the University of T{\"u}bingen and put in its final form at the AEI Golm and the ETH Z{\"u}rich. AEI publication number: AEI-2008-063.",

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PY - 2009/7

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N2 - In this work the isoperimetric inequality for integral varifolds of locally bounded first variation is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calderón's and Zygmund's theory of first order differentiability for functions in Lebesgue spaces from Lebesgue measure to integral varifolds.

AB - In this work the isoperimetric inequality for integral varifolds of locally bounded first variation is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calderón's and Zygmund's theory of first order differentiability for functions in Lebesgue spaces from Lebesgue measure to integral varifolds.

KW - Height-excess

KW - Integral varifolds

KW - Locally bounded first variation

KW - Tilt-excess

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Some applications of the isoperimetric inequality for integral varifolds

Abstract

Keywords

ASJC Scopus subject areas

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