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15 August 2020 The limit shape of convex hull peeling
Jeff Calder, Charles K. Smart
Duke Math. J. 169(11): 2079-2124 (15 August 2020). DOI: 10.1215/00127094-2020-0013

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 (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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Jeff Calder. Charles K. Smart. "The limit shape of convex hull peeling." Duke Math. J. 169 (11) 2079 - 2124, 15 August 2020. https://doi.org/10.1215/00127094-2020-0013

Information

Received: 29 November 2018; Revised: 1 December 2019; Published: 15 August 2020
First available in Project Euclid: 27 June 2020

MathSciNet: MR4132581
Digital Object Identifier: 10.1215/00127094-2020-0013

Subjects:
Primary: 35D40
Secondary: 35B27, 53C44, 68Q87, 91A05, 97K50

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 11 • 15 August 2020
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