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Determination of sets with positive reach by their projection type images
-
Vladimir Golubyatnikov
and
Vladimir Rovenski
Published/Copyright:
August 5, 2011
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
Received: 2010-12-14
Published Online: 2011-08-05
Published in Print: 2011-August
© de Gruyter 2011
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Keywords for this article
Set with positive reach;
convex body;
support ball;
Hausdorff distance;
stability theorem;
geometric tomography
Articles in the same Issue
- Logarithmic convergence rate of Levenberg–Marquardt method with application to an inverse potential problem
- Regularization and error estimate for a spherically symmetric backward heat equation
- Inverse problem and null-controllability for parabolic systems
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- Exponential instability in the Gel'fand inverse problem on the energy intervals
- A generalization of continuous regularized Gauss–Newton method for ill-posed problems
- Direct and inverse problems of the theory of wave propagation in an elastic inhomogeneous medium
- Determination of the unknown time dependent coefficient p(t) in the parabolic equation ut = Δu + p(t)u + φ(x, t)
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- International Conference “Inverse and Ill-Posed Problems of Mathematical Physics” dedicated to the 80th birthday of Academician M. M. Lavrentiev
- The Sixth International Conference “Inverse Problems: Modeling & Simulation”
- Third International Scientific Conference and Young Scientists School “Theory and Computational Methods for Inverse and Ill-Posed Problems”
