Some Applications of the Isoperimetric Inequality for Integral Varifolds

Abstract

In this work the Isoperimetric Inequality for integral varifolds 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.

arXiv comment15 pages, no figures

References in corpus (2)

• Second order rectifiability of integral varifolds of locally bounded first variation
• A Sobolev Poincaré type inequality for integral varifolds

Cited by in corpus (12)

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• A Sobolev Poincaré type inequality for integral varifolds
• Decay estimates for the quadratic tilt-excess of integral varifolds
• Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds
• Some geometric inequalities for varifolds on Riemannian manifolds based on monotonicity identities
• Sobolev functions on varifolds
• Pointwise differentiability of higher order for sets
• A new version of Brakke's local regularity theorem
• Estimating discrete curvatures in terms of beta numbers
• Cubical Covers of Sets in ${\mathbb{R}}^n$