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When do sections of different dimensions determine a convex body?

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Alessandro Soranzo  and
Aljoša Volčič
Alessandro Soranzo
Affiliation:
Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, 34127 Trieste. Italy. E-mail: soranzo@univ.trieste.it
Aljoša Volčič
Affiliation:
Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, 34127 Trieste, Italy
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Abstract

This paper gives a partial answer to a problem posed by Volčič and shows, in particular, that a three-dimensional convex body K is uniquely determined if p′ and p″ are two points interior to K and the lengths of all the chords of K through p′ and the areas of all sections of K with planes through p″ are known, provided that a specific condition on the positions of p′ and p″ with respect to K is satisfied. The problem will be studied in the more general framework of i-chord functions, and the results will also cover cases where the points p′ and p″ are not interior to K, possibly with one of them at infinity.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 50 , Issue 1-2 , December 2003 , pp. 35 - 55
Copyright
Copyright © University College London 2003

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