Calculus of Variations and Geometric Measure Theory
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M. Santilli

Second order rectifiability of varifolds of bounded mean curvature

created by santilli on 21 Jul 2020
modified on 14 Jun 2021


Published Paper

Inserted: 21 jul 2020
Last Updated: 14 jun 2021

Journal: Calc. Var. Partial Differential Equations
Year: 2021

ArXiv: 1907.02792 PDF


We prove that the support of an $ m $ dimensional rectifiable varifold with a uniform lower bound on the density and bounded generalized mean curvature can be covered $ \mathscr{H}^{m} $ almost everywhere by a countable union of $m$ dimensional submanifolds of class $ \mathcal{C}^{2} $. We obtain this result using the notion of curvature of arbitrary closed sets originally developed in stochastic geometry and extending to our geometric setting techniques developed by Trudinger in the theory of viscosity solutions of PDE's.

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