The limit shape of convex hull peeling
May 21, 2018 Β· Declared Dead Β· π Duke mathematical journal
"No code URL or promise found in abstract"
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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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