Equivariant Maps and Some Problems of the Geometry of Convex Sets

A. Yu. Volovikov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 83-97.

Résumé

Methods of equivariant topology are applied to some problems of convex set geometry. In particular, it is proved that a pyramid homothetic to a regular pyramid of certain type with a regular $p$-gon as the base, where $p$ is an odd prime, can be inscribed in any convex $(p+5)/2$-dimensional body.

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