Decay estimates for the quadratic tilt-excess of integral varifolds

Abstract

This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space with its first variation given by either a Radon measure or a function in some Lebesgue space. Pointwise decay results for the quadratic tilt-excess are established for those varifolds. The results are optimal in terms of the dimension of the varifold and the exponent of the Lebesgue space in most cases, for example if the varifold is not two-dimensional.

v3: major revision; new section "Preliminaries"; new section "A model case of partial regularity"; introduction, notation and 5.1-5.4 revised; some additional remarks and references. 79 pages, no figures

References in corpus (4)

• Pathological solutions to elliptic problems in divergence form with continuous coefficients
• Second order rectifiability of integral varifolds of locally bounded first variation
• Some Applications of the Isoperimetric Inequality for Integral Varifolds
• A Sobolev Poincaré type inequality for integral varifolds

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• Pointwise differentiability of higher order for sets
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• Estimating discrete curvatures in terms of beta numbers
• Cubical Covers of Sets in ${\mathbb{R}}^n$
• Universal moduli of continuity for solutions to fully nonlinear elliptic equations