Journal
DUKE MATHEMATICAL JOURNAL
Volume 169, Issue 11, Pages 2079-2124Publisher
DUKE UNIV PRESS
DOI: 10.1215/00127094-2020-0013
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Funding
- National Science Foundation (NSF) [DMS-1500829]
- NSF [DMS-1712841]
- Alfred P. Sloan Foundation
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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 (PDE). We use the martingale method to solve the cell problem associated to convex peeling. Our proof follows the program of Armstrong and Cardaliaguet for homogenization of geometric motions, but with completely different ingredients.
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