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NON-UNIQUENESS OF CONVEX BODIES WITH PRESCRIBED VOLUMES OF SECTIONS AND PROJECTIONS

Part of: General convexity

Published online by Cambridge University Press:  01 August 2012

Fedor Nazarov ,
Dmitry Ryabogin  and
Artem Zvavitch
Fedor Nazarov
Affiliation:
Department of Mathematics, Kent State University, Kent, OH 44242, U.S.A. (email: nazarov@math.kent.edu)
Dmitry Ryabogin
Affiliation:
Department of Mathematics, Kent State University, Kent, OH 44242, U.S.A. (email: ryabogin@math.kent.edu)
Artem Zvavitch
Affiliation:
Department of Mathematics, Kent State University, Kent, OH 44242, U.S.A. (email: zvavitch@math.kent.edu)
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Abstract

We show that if d≥4 is even, then one can find two essentially different convex bodies such that the volumes of their maximal sections, central sections, and projections coincide for all directions.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces) 52A40: Inequalities and extremum problems 52A38: Length, area, volume
Type
Research Article
Information
Mathematika , Volume 59 , Issue 1 , January 2013 , pp. 213 - 221
Copyright
Copyright © University College London 2012

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References

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