Rogers–Shephard and local Loomis–Whitney type inequalities

Rogers–Shephard and local Loomis–Whitney type inequalities

We provide functional analogues of the classical geometric inequality of Rogers and Shephard on products of volumes of sections and projections. As a consequence we recover (and obtain some new) functional versions of Rogers–Shephard type inequalities as well as some generalizations of the geometric...

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Veröffentlicht in:Mathematische annalen 2019-08, Vol.374 (3-4), p.1719-1771
Hauptverfasser: Alonso-Gutiérrez, David, Artstein-Avidan, Shiri, González Merino, Bernardo, Jiménez, Carlos Hugo, Villa, Rafael
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Inequalities
Inequality
Mathematics
Mathematics and Statistics
Subspaces
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container_end_page 1771
container_issue 3-4
container_start_page 1719
container_title Mathematische annalen
container_volume 374
creator Alonso-Gutiérrez, David
Artstein-Avidan, Shiri
González Merino, Bernardo
Jiménez, Carlos Hugo
Villa, Rafael
description We provide functional analogues of the classical geometric inequality of Rogers and Shephard on products of volumes of sections and projections. As a consequence we recover (and obtain some new) functional versions of Rogers–Shephard type inequalities as well as some generalizations of the geometric Rogers–Shephard inequality in the case where the subspaces intersect. These generalizations can be regarded as sharp local reverse Loomis–Whitney inequalities. We also obtain a sharp local Loomis–Whitney inequality.
doi_str_mv 10.1007/s00208-019-01834-3
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subjects Inequalities
Inequality
Mathematics
Mathematics and Statistics
Subspaces
title Rogers–Shephard and local Loomis–Whitney type inequalities
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