Inequalities Between the Radii of Some Spheres That Are Connected with a Convex Surface in Space of Constant Curvature

Abstract

With a convex surface Φ in space of constant curvature, we associate four numbers (λ,ΛM,μ), where μ is the radius of a largerst sphere freely rolling over the interior side of Φ, Λ is the inradius of Φ, M is the outradius of Φ, and μ is the radius of a sphere over whose interior Φ may roll freely. Exact inequalities connecting these four numbers are found.