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 language | English (US) |
|---|---|
| Pages (from-to) | 2079-2124 |
| Number of pages | 46 |
| Journal | Duke Mathematical Journal |
| Volume | 169 |
| Issue number | 11 |
| DOIs | |
| State | Published - 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.
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