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The Lower Dimensional Busemann-Petty Problem with Weights

Part of: Integral transforms, operational calculus General convexity

Published online by Cambridge University Press:  21 December 2009

Boris Rubin
Boris Rubin
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, U.S.A. E-mail: borisr@math.lsu.edu
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Abstract

The lower dimensional Busemann-Petty problem asks whether origin-symmetric convex bodies in ℝ n with smaller i-dimensional central sections necessarily have smaller volume. A generalization of this problem is studied, when the volumes are measured with weights satisfying certain conditions. The case of hyperplane sections (i = n − 1) has been studied by A. Zvavitch.

MSC classification

Secondary: 52A38: Length, area, volume 44A12: Radon transform
Type
Research Article
Information
Mathematika , Volume 53 , Issue 2 , December 2006 , pp. 235 - 245
Copyright
Copyright © University College London 2006

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