The limit shape of convex hull peeling

Jeff Calder, Charles K. Smart

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that the convex peeling of a random point set in dimension d approximates motion by the 1/(d + ) 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.

Original languageEnglish (US)
Pages (from-to)2079-2124
Number of pages46
JournalDuke Mathematical Journal
Volume169
Issue number11
DOIs
StatePublished - Aug 15 2020

Bibliographical note

Funding Information:
Acknowledgments. Calder’s work was partially supported by National Science Foundation (NSF) grant DMS-1500829. Smart’s work was partially supported by NSF grant DMS-1712841 and by the Alfred P. Sloan Foundation.

Publisher Copyright:
© 2020 Duke University Press. All rights reserved.

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