A Sobolev Poincaré type inequality for integral varifolds

Abstract

In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown to be sharp.

v1: 27 pages, no figures; v2: replaced citations of the author's dissertation by proofs, material of sections 1 and 3 reorganised, slightly more general results in section 2, some remarks, some discussion and some references added, 40 pages, no figures

References in corpus (2)

• Q-valued functions revisited
• Some Applications of the Isoperimetric Inequality for Integral Varifolds

Cited by in corpus (10)

• Second order rectifiability of integral varifolds of locally bounded first variation
• Weakly differentiable functions on varifolds
• Some Applications of the Isoperimetric Inequality for Integral Varifolds
• Existence of solutions to a general geometric elliptic variational problem
• Decay estimates for the quadratic tilt-excess of integral varifolds
• Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds
• Sobolev functions on varifolds
• Pointwise differentiability of higher order for sets
• Estimating discrete curvatures in terms of beta numbers
• Cubical Covers of Sets in ${\mathbb{R}}^n$