Rogers–Shephard and local Loomis–Whitney type inequalities

David Alonso-Gutiérrez, Shiri Artstein-Avidan, Bernardo González Merino, Carlos Hugo Jiménez, Rafael Villa

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1719-1771
Number of pages53
JournalMathematische Annalen
Issue number3-4
StatePublished - 6 Aug 2019


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