TY - JOUR
T1 - Rogers–Shephard and local Loomis–Whitney type inequalities
AU - Alonso-Gutiérrez, David
AU - Artstein-Avidan, Shiri
AU - González Merino, Bernardo
AU - Jiménez, Carlos Hugo
AU - Villa, Rafael
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/8/6
Y1 - 2019/8/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85065430274&partnerID=8YFLogxK
U2 - 10.1007/s00208-019-01834-3
DO - 10.1007/s00208-019-01834-3
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AN - SCOPUS:85065430274
VL - 374
SP - 1719
EP - 1771
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 3-4
ER -