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On a convexity property of sections of the cross-polytope


Authors: Piotr Nayar and Tomasz Tkocz
Journal: Proc. Amer. Math. Soc. 148 (2020), 1271-1278
MSC (2010): Primary 52A40; Secondary 52A20
DOI: https://doi.org/10.1090/proc/14777
Published electronically: September 23, 2019
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Abstract: We establish the log-concavity of the volume of central sections of dilations of the cross-polytope (the strong B-inequality for the cross-polytope and Lebesgue measure restricted to an arbitrary subspace).


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Additional Information

Piotr Nayar
Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
Email: nayar@mimuw.edu.pl

Tomasz Tkocz
Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Email: ttkocz@math.cmu.edu

DOI: https://doi.org/10.1090/proc/14777
Keywords: Cross-polytope, volume of sections, logarithmic Brunn-Minkowski inequality
Received by editor(s): February 27, 2019
Received by editor(s) in revised form: July 16, 2019
Published electronically: September 23, 2019
Communicated by: Deane Yang
Article copyright: © Copyright 2019 American Mathematical Society