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Mathematics > Metric Geometry

Title: Higher-Order Reverse Isoperimetric Inequalities for Log-concave Functions

Authors: Dylan Langharst, Francisco Marín Sola, Jacopo Ulivelli
(Submitted on 8 Mar 2024 (v1), last revised 23 Mar 2024 (this version, v3))
Abstract: The Rogers-Shephard and Zhang's projection inequalities are two reverse, affine isoperimetric inequalities relating the volumes of a convex body and its difference body and polar projection body, respectively. Following a classical work by Schneider, both inequalities have been extended to the so-called higher-order setting. In this work, we establish the higher-order analogues for these inequalities in the setting of log-concave functions.
Comments: 25 pages; (v2-3): modifications of presentation
Subjects: Metric Geometry (math.MG); Functional Analysis (math.FA)
MSC classes: Primary: 26B25, 52A38, 52A40, Secondary: 52A20
Cite as: arXiv:2403.05712 [math.MG]
  (or arXiv:2403.05712v3 [math.MG] for this version)

Submission history

From: Dylan Langharst [view email]
[v1] Fri, 8 Mar 2024 22:59:13 GMT (60kb)
[v2] Wed, 20 Mar 2024 07:56:12 GMT (60kb)
[v3] Sat, 23 Mar 2024 18:37:31 GMT (60kb)
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