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arXiv · 2606.06291

Mixed Minkowski-Covering Inequalities for Convex Bodies and Lattices

Aled Williams
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Abstract

In this paper we present a sharp mixed inequality relating successive minima and quotient covering radii of origin-symmetric convex bodies with respect to lattices. The inequality interpolates between the (classical) covering-density lower bound and the lower bound in Minkowski's second theorem.

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Aled Williams. 2026-06-04. Mixed Minkowski-Covering Inequalities for Convex Bodies and Lattices. https://arxiv.org/abs/2606.06291

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