TY - JOUR
T1 - Projective transformations of convex bodies and volume product
AU - Balacheff, Florent
AU - Solanes, Gil
AU - Tzanev, Kroum
N1 - Publisher Copyright:
© The Author(s) 2024. Published by Oxford University Press. All rights reserved.
PY - 2024/6/1
Y1 - 2024/6/1
N2 - 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 2 containing saddle points for this functional.
AB - 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 2 containing saddle points for this functional.
UR - https://www.mendeley.com/catalogue/6b261ba5-6df5-3df8-ad35-1f7e50db1690/
UR - http://www.scopus.com/inward/record.url?scp=85195795420&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnad310
DO - 10.1093/imrn/rnad310
M3 - Article
SN - 1073-7928
VL - 2024
SP - 9054
EP - 9065
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 11
M1 - rnad310
ER -