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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 19, Issue 3 (Jan 2011)


Determination of sets with positive reach by their projection type images

Vladimir Golubyatnikov
  • Sobolev Institute of Mathematics, Akademician Koptyg str. 4, Novosibirsk, 630090, Russia.
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/ Vladimir Rovenski
  • Mathematical Department, University of Haifa, Haifa, 31905, Israel.
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Published Online: 2011-08-05 | DOI: https://doi.org/10.1515/jiip.2011.037


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

About the article

Received: 2010-12-14

Published Online: 2011-08-05

Published in Print: 2011-08-01

Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2011.037. Export Citation

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