S. Arya

collaborators

5 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…

math.MG2026

On the Duality of Coverings in Hilbert Geometry

Sunil Arya, David M. Mount

We prove polarity duality for covering problems in Hilbert geometry. Let $G$ and $K$ be convex bodies in $R^{d}$ where $G \subset int (K)$ and $\operatorname{i…

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…

cs.CG2025

Optimal Volume-Sensitive Bounds for Polytope Approximation

Sunil Arya, David M. Mount

Approximating convex bodies is a fundamental question in geometry, which has a wide variety of applications. Given a convex body $K$ in $R^{d}$ for fixed $d$ , the objective…