The limit shape of convex hull peeling

May 21, 2018 Β· Declared Dead Β· πŸ› Duke mathematical journal

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Authors Jeff Calder, Charles K Smart arXiv ID 1805.08278 Category math.AP Cross-listed cs.DS, math.NA, math.PR Citations 28 Venue Duke mathematical journal Last Checked 1 month ago
Abstract
We prove that the convex peeling of a random point set in dimension d approximates motion by the 1/(d + 1) power of Gaussian curvature. We use viscosity solution theory to interpret the limiting partial differential equation. We use the Martingale method to solve the cell problem associated to convex peeling. Our proof follows the program of Armstrong-Cardaliaguet for homogenization of geometric motions, but with completely different ingredients.
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