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Mean Convex Smoothing of Mean Convex Cones (2202.07851v1)
Published 16 Feb 2022 in math.DG and math.AP
Abstract: We show that any minimizing hypercone can be perturbed into one side to a properly embedded smooth minimizing hypersurface in the Euclidean space, and every viscosity mean convex cone admits a properly embedded smooth mean convex self-expander asymptotic to it near infinity. These two together confirm a conjecture of Lawson \cite[Problem 5.7]{Brothers86_OpenProblems}.
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