Volume inequalities for isotropic measures
By Erwin Lutwak, Deane Yang, Gaoyong Zhang. 2006
79 citations recorded by the source corpus.
A direct approach to Ball's simplex inequality is presented. This approach, which does not use the Brascamp-Lieb inequality, also gives Barthe's characterization of the simplex for Ball's inequality and extends it from discrete to arbitrary measures. It also yields the dual inequality, along with equality conditions, and it does both for arbitrary measures.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9546a3a8e660302071d81a60c5ef3e008c32e825
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In Applied Mathematics
- Yiming Zhao
- Franz E. Schuster
- Gaoyong Zhang
- Deane Yang
- Erwin Lutwak
- Manuel Weberndorfer
- Monika Ludwig
- Deping Ye
In Geometry and Topology
- Yiming Zhao
- Franz E. Schuster
- Deane Yang
- Gaoyong Zhang
- Erwin Lutwak
- Manuel Weberndorfer
- Monika Ludwig
- Deping Ye
Citations in the corpus
- Volume inequalities for asymmetric Wulff shapes (2011, methodology): “In Section 6 we show how Theorems 1 and 2 directly imply a number of reverse isoperimetric inequalities (including all equality conditions) obtained by Ball [1, 2], Barthe [4] and Lutwak, Yang, Zhang [29, 31, 32].”
- The log-Brunn-Minkowski inequality (2012, unknown): “[5,8–12,16,18,22–30,32–55,58,62–65,67–69]).”
- Lp John Ellipsoids (2005, background): “A direct proof of the inequality can be found in [36] (see also [37]).”
- Cone-volume measure of general centered convex bodies (2016, unknown): “Zhang [31,33].”
- Shadow systems of asymmetric Lp zonotopes (2013, unknown): “[9,12,21,23,26–30,32,35–37,44,46–48,51]).”
- The even Orlicz-Minkowski problem (2010, unknown): “[1–5, 7–10, 12, 13, 15–22, 25–39, 41–44, 47, 49, 50, 52–55, 58, 60–63, 65–68]).”