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When do sections of different dimensions determine a convex body?
Published online by Cambridge University Press: 26 February 2010
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.
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- Research Article
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- Copyright © University College London 2003