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VOLUMES OF PROJECTION BODIES OF SOME CLASSES OF CONVEX BODIES

Published online by Cambridge University Press:  20 June 2011

Christos Saroglou*
Affiliation:
Department of Mathematics, University of Crete, Greece (email: [email protected])
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Abstract

Schneider posed the problem of determining the maximal value of the affine invariant ∣ΠK∣/∣Kd−1, where ΠK is the projection body of the d-dimensional convex body K. Some three-dimensional conjectures of Brannen, related to Schneider’s problem, are confirmed. Namely, we determine the maximal value of ∣ΠK∣/∣K2 in the class of three-dimensional zonoids, cones and double cones. Equality cases are, also, investigated. Moreover, results related to a conjecture of Petty, concerning the minimal value of the above quantity, are obtained. In particular, we provide a negative answer to a question of Martini and Mustafaev.

Type
Research Article
Copyright
Copyright © University College London 2011

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