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When do sections of different dimensions determine a convex body?

Published online by Cambridge University Press:  26 February 2010

Alessandro Soranzo
Affiliation:
Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, 34127 Trieste. Italy. E-mail: [email protected]
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.

Type
Research Article
Copyright
Copyright © University College London 2003

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