TY - JOUR
T1 - Isobarycentric Inequalities
AU - Gilboa, Shoni
AU - Haim-Kislev, Pazit
AU - Slomka, Boaz A.
N1 - Publisher Copyright:
© 2022 The Author(s). Published by Oxford University Press. All rights reserved.
PY - 2023/7/1
Y1 - 2023/7/1
N2 - We prove the following isoperimetric-type inequality: Given a finite absolutely continuous Borel measure on, half-spaces have maximal measure among all subsets with prescribed barycenter. As a consequence, we make progress towards a solution to a problem of Henk and Pollehn, which is equivalent to a log-Minkowski inequality for a parallelotope and a centered convex body. Our probabilistic approach to the problem also gives rise to several inequalities and conjectures concerning the truncated mean of certain log-concave random variables.
AB - We prove the following isoperimetric-type inequality: Given a finite absolutely continuous Borel measure on, half-spaces have maximal measure among all subsets with prescribed barycenter. As a consequence, we make progress towards a solution to a problem of Henk and Pollehn, which is equivalent to a log-Minkowski inequality for a parallelotope and a centered convex body. Our probabilistic approach to the problem also gives rise to several inequalities and conjectures concerning the truncated mean of certain log-concave random variables.
UR - http://www.scopus.com/inward/record.url?scp=85166252824&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnac191
DO - 10.1093/imrn/rnac191
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AN - SCOPUS:85166252824
SN - 1073-7928
VL - 2023
SP - 12298
EP - 12323
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 14
ER -