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arXiv · 2602.15352

From Blaschke--Santal\'o-type inequalities to uniform contractions

Károly Bezdek
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Abstract

In this short note, we establish Blaschke--Santal\'o-type inequalities for $r$-ball bodies. Building on these inequalities, we somewhat further extend earlier results on analogues of the Kneser--Poulsen conjecture concerning intersections of balls under uniform contractions in Euclidean $d$-space. As an immediate corollary, we obtain a proof of Alexander's conjecture for uniform contractions.

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Károly Bezdek. 2026-02-17. From Blaschke--Santal\'o-type inequalities to uniform contractions. https://arxiv.org/abs/2602.15352

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