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ABP inequalities for singular submanifolds of bounded mean curvature

Published 6 Sep 2018 in math.AP and math.DG | (1809.02198v1)

Abstract: Employing a notion of curvature for arbitrary closed sets we prove an ABP-type estimate for a class of singular submanifolds of arbitrary codimension and bounded mean curvature recently introduced by B. White. A weak-Harnack-type estimate is then derived using the ABP estimate. These results generalize analogous results by O. Savin for viscosity solutions of the minimal surface equation.

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