A.D. Alexandrov's conjecture and hyperbolic virtual polytopes

Gaiane Panina
Bielefeld
St. Petersburg

Abstract.
Hyperbolic virtual polytopes appeared as an auxiliary
tool for constructing counterexamples to the following
A.D. Alexandrov's conjecture (1938):

Given a smooth compact convex body K in R3, if a constant C
separates (non-strictly) its principal curvatures at every
point of its boundary, then K is a ball.

We shall show that the problem has a combinatorial background.

The talk is based on the papers of Y. Martinez-Maure and
the speaker.