David M. Mount

collaborators

4 papers

math.MG2026

Duality Bounds for Convexified Packing in Hilbert Geometry

Sunil Arya, David M. Mount

Let $G$ and $K$ be convex bodies in $R^{d}$ , where $0 \in int G$ and $G \subset int K$ . Given $α > 0$ , the Hilbert packing number $M_{H} (G, K; α)$ is the maximum…

cs.CG2026

Differentiable Approximations for Distance Queries

Ahmed Abdelkader, David M. Mount

The widespread use of gradient-based optimization has motivated the adaptation of various classical algorithms into differentiable solvers compatible with learning pipelines. In th…

cs.CG2026

Cauchy's Surface Area Formula in the Funk Geometry

Sunil Arya, David M. Mount

Cauchy's surface area formula expresses the surface area of a convex body as the average area of its orthogonal projections over all directions. While this tool is fundamental in E…

cs.CG2025

Optimal Area-Sensitive Bounds for Polytope Approximation

Sunil Arya, Guilherme D. da Fonseca, David M. Mount

Approximating convex bodies is a fundamental problem in geometry. Given a convex body $K$ in $R^{d}$ for a fixed dimension $d$ , the objective is to minimize the number of fa…