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

Pál'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.