Moscow--Petersburg
seminar on low-dimensional mathematics
SPb, PDMI, 16.11.2001, 16:00--17:45, room 311

Virtual polytopes and some classical problems of geometry.
G. Panina

A virtual polytope is the Minkowski difference of two convex polytopes.
We consider  some problems (the Minkowski theorem, flexibility,
properties of the fan and perhaps Gale diagrams) for virtual polytopes.

We also consider from this viewpoint the following old hypothesis.
A smooth convex body whose principal curvatures K1 and K2 satisfy
the inequality  K1 \le C \le K2  with some constant C,
is necessarily  a sphere.

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Seminar home-page http://www.pdmi.ras.ru/~duzhin/lowdimma.html