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Projective transformations of convex bodies and volume product
Balacheff, Florent Nicolas (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Solanes, Gil (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tzanev, Kroum (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date: 2024
Abstract: In this paper, we study certain variational aspects of the volume product functional restricted to the space of small projective deformations of a fixed convex body. In doing so, we provide a short proof of a theorem by Klartag: a strong version of the slicing conjecture implies the non-symmetric Mahler conjecture. We also exhibit an interesting family of critical convex bodies in dimension containing saddle points for this functional.
Grants: Ministerio de Economía, Industria y Competitividad RYC-2016-19334
Ministerio de Ciencia e Innovación CEX2020-001084-M
Agencia Estatal de Investigación PID2021-125625NB-I00
Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-01015
Rights: Tots els drets reservats.
Language: Anglès
Document: Article ; recerca ; Versió acceptada per publicar
Published in: International Mathematics Research Notices, ISSN 1687-0247

DOI: 10.1093/imrn/rnad310


Available from: 2025-01-31
Postprint

The record appears in these collections:
Articles > Research articles
Articles > Published articles

 Record created 2024-01-25, last modified 2024-05-04



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