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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Determination of sets with positive reach by their projection type images

1Sobolev Institute of Mathematics, Akademician Koptyg str. 4, Novosibirsk, 630090, Russia.

2Mathematical Department, University of Haifa, Haifa, 31905, Israel.

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 19, Issue 3, Pages 407–428, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2011.037, August 2011

Publication History

Received:
2010-12-14
Published Online:
2011-08-05

Abstract

We introduce new classes of sets extending the class of convex bodies. We show strong inclusions between these classes of bodies. In the case of bodies in Euclidean spaces, we obtain a new characterization of sets with positive reach, prove the Helly type theorem for them, and find applications to geometric tomography. We investigate the problem of determination of sets with positive reach by their projection-type images, and generalize corresponding stability theorems by H. Groemer.

Keywords.: Set with positive reach; convex body; support ball; Hausdorff distance; stability theorem; geometric tomography

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