# The limit shape of convex hull peeling

arXiv: https://arxiv.org/abs/1805.08278 · HTML: https://mlsanity.com/paper/1805.08278/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2018.

## Built on by (most cited first, 6 of 6)

- [Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depth](https://mlsanity.com/paper/2202.08789/) (2022)
- [Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications](https://mlsanity.com/paper/2111.03217/) (2021)
- [Tukey Depths and Hamilton-Jacobi Differential Equations](https://mlsanity.com/paper/2104.01648/) (2021)
- [Numerical solution of a PDE arising from prediction with expert advice](https://mlsanity.com/paper/2406.05754/) (2024)
- [Eikonal depth: an optimal control approach to statistical depths](https://mlsanity.com/paper/2201.05274/) (2022)
- [RACH-Space: Reconstructing Adaptive Convex Hull Space with Applications in Weak Supervision](https://mlsanity.com/paper/2307.04870/) (2023)

## Abstract (arXiv)

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.