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arXiv · 2602.19300

P\'al's isominwidth inequality for ball convex bodies in planes of constant curvature

Ferenc Fodor·Nathan Robock·Ádám Sagmeister
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Abstract

P\'al's classical isominwidth inequality states that the regular triangle has minimal area among plane convex bodies of minimal width $w$. A similar result is the Blaschke--Lebesgue inequality that states that Reuleaux triangles minimize the area among bodies of constant width $w$ in the plane. In this paper, we connect these two problems by solving the isominwidth problem for $r$-ball convex bodies in the Euclidean, hyperbolic and spherical planes.

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Ferenc Fodor, Nathan Robock, Ádám Sagmeister. 2026-02-22. P\'al's isominwidth inequality for ball convex bodies in planes of constant curvature. https://arxiv.org/abs/2602.19300

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