Inequalities between the radii of spheres that are connected with a convex surface in a space of constant curvature

V. K. Ionin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: With a convex surface $\Phi$ in space of constant curvature, we associate four numbers ($\lambda$, $\Lambda$, $M$, $\mu$), where $\lambda$ is the radius of a largerst sphere freely rolling over the interior side of $\Phi$, $\Lambda$ is the inradius of $\Phi$, $M$ is the outradius of $\Phi$, and $\mu$ is the radius of a sphere over whose interior $\Phi$ may roll freely. Exact inequalities connecting these four numbers are found.

UDC: 514.17

Received: 09.06.2000

 English version: Siberian Mathematical Journal, 2001, 42:3, 473–477

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