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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the volume of sections of a convex body by cones
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by Matthieu Fradelizi, Mathieu Meyer and Vlad Yaskin PDF
Proc. Amer. Math. Soc. 145 (2017), 3153-3164 Request permission

Abstract:

We prove that in small codimensions, the sections of a convex body in $\mathbb R^n$ through its centroid are quite symmetric with respect to volume. As a consequence of our estimates we give a positive answer to a problem posed by M. Meyer and S. Reisner regarding convex intersection bodies.
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Additional Information
  • Matthieu Fradelizi
  • Affiliation: Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées UMR 8050, UPEMLV, UPEC, CNRS F-77454, Marne-la-Vallée, France
  • MR Author ID: 626525
  • Email: matthieu.fradelizi@u-pem.fr
  • Mathieu Meyer
  • Affiliation: Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées UMR 8050, UPEMLV, UPEC, CNRS F-77454, Marne-la-Vallée, France
  • MR Author ID: 197612
  • Email: mathieu.meyer@u-pem.fr
  • Vlad Yaskin
  • Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
  • MR Author ID: 650371
  • Email: yaskin@ualberta.ca
  • Received by editor(s): April 12, 2016
  • Received by editor(s) in revised form: August 29, 2016
  • Published electronically: January 23, 2017
  • Additional Notes: The third author was supported in part by NSERC. Part of this work was done when the third author was visiting Université Paris-Est Marne-la-Vallée. He is grateful for its hospitality
  • Communicated by: Thomas Schlumprecht
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 3153-3164
  • MSC (2010): Primary 52A20, 52A40
  • DOI: https://doi.org/10.1090/proc/13457
  • MathSciNet review: 3637961