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Accessible Unlicensed Requires Authentication Published by De Gruyter August 5, 2011

Determination of sets with positive reach by their projection type images

Vladimir Golubyatnikov and Vladimir Rovenski
From the journal

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.

Received: 2010-12-14
Published Online: 2011-08-05
Published in Print: 2011-August

© de Gruyter 2011