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Volume difference inequalities


Authors: Apostolos Giannopoulos and Alexander Koldobsky
Journal: Trans. Amer. Math. Soc. 370 (2018), 4351-4372
MSC (2010): Primary 52A20; Secondary 46B06
DOI: https://doi.org/10.1090/tran/7173
Published electronically: February 19, 2018
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Abstract: We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is replaced by an arbitrary measure.


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Additional Information

Apostolos Giannopoulos
Affiliation: Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis 157-84, Athens, Greece
Email: apgiannop@math.uoa.gr

Alexander Koldobsky
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: koldobskiya@missouri.edu

DOI: https://doi.org/10.1090/tran/7173
Keywords: Convex bodies, Busemann-Petty problem, Shephard problem, sections, projections, volume difference inequalities, intersection bodies, isotropic convex body
Received by editor(s): August 11, 2016
Received by editor(s) in revised form: December 17, 2016
Published electronically: February 19, 2018
Additional Notes: The second named author was supported in part by the NSF grant DMS-1265155
Article copyright: © Copyright 2018 American Mathematical Society

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