Jump to ContentJump to Main Navigation

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year

Increased IMPACT FACTOR 2013: 0.593
Rank 143 out of 299 in category Mathematics in the 2013 Thomson Reuters Journal Citation Report/Science Edition
Mathematical Citation Quotient 2013: 0.51

VolumeIssuePage

Issues

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

Comments (0)

Please log in or register to comment.
Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.