ABP inequalities for singular submanifolds of bounded mean curvature
classification
🧮 math.AP
math.DG
keywords
curvatureestimatearbitraryboundedmeanresultssingularsubmanifolds
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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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