Second order rectifiability of integral varifolds of locally bounded first variation

Abstract

In this work it is shown that every integral varifold in an open subset of Euclidian space of locally bounded first variation can be covered by a countable collection of submanifolds of class C^2. Moreover, the mean curvature of each member of the collection agrees with the mean curvature of the varifold almost everywhere with respect to the varifold.

v1: 34 pages, no figures; v2: revised presentation, material of 0909.3253 and 0808.3665 reorganised, parts moved to 0909.3253v2, parts from 0909.3253v1 included, this version now depends on 0909.3253v2, comparison to Hutchinson's second fundamental form added, 40 pages, no figures; v3: introduction and 4.5 revised, 3.8 and one reference added, one reference updated, 40 pages, no figures

References in corpus (4)

• Some Applications of the Isoperimetric Inequality for Integral Varifolds
• A Sobolev Poincaré type inequality for integral varifolds
• Decay estimates for the quadratic tilt-excess of integral varifolds
• Convergence of perturbed Allen-Cahn equations to forced mean curvature flow

Cited by in corpus (18)

• Weakly differentiable functions on varifolds
• Rectifiability and approximate differentiability of higher order for sets
• Some Applications of the Isoperimetric Inequality for Integral Varifolds
• Characterizing $W^{2,p}$~submanifolds by $p$-integrability of global curvatures
• Existence of Integral $m$-Varifolds minimizing $\int |A{|}^p$ and $\int |H{|}^p$, $p>m$, in Riemannian Manifolds
• Decay estimates for the quadratic tilt-excess of integral varifolds
• Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds
• On a isoperimetric-isodiametric inequality
• On the existence of canonical multi-phase Brakke flows
• Second order rectifiability of varifolds of bounded mean curvature
• Sobolev functions on varifolds
• Pointwise differentiability of higher order for sets
• The spherical image of singular varieties of bounded mean curvature
• The concept of varifold
• Pointwise differentiability of higher order for distributions
• Curvature-dependent Eulerian interfaces in elastic solids
• Rectifiability; a survey
• Integral decompositions of varifolds