On convexity of a planar domain with a pair of concave tomography projections

V. P. Golubyatnikov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We describe simple sufficient conditions on tomography-type measurements of a planar set which imply convexity of this set. The cases of partial convexity and higher-dimensional sets are considered as well.

Key words: convexity, concavity, geometric tomography, rearrangement of a function.

UDC: 514.17

Received: 07.12.2007

 English version: Siberian Advances in Mathematics, 2009, 19:2, 85–90

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