The Lp-Busemann–Petty Centroid Inequality
By S. Campi, Paolo Gronchi. 2002
243 citations recorded by the source corpus.
Subfields: Applied Mathematics, Pharmacology
View Paper: https://www.semanticscholar.org/paper/fae90ef0bea0c074167f43465475c1a894f70dcb
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Monika Ludwig
- Yiming Zhao
- Christoph Haberl
- Gaoyong Zhang
- Deane Yang
- Erwin Lutwak
- Franz E. Schuster
- Deping Ye
In Pharmacology
- Monika Ludwig
- Christoph Haberl
- Gaoyong Zhang
- Deane Yang
- Erwin Lutwak
- Ai-jun Li
- Gangsong Leng
- Franz E. Schuster
Citations in the corpus
- Affine Moser–Trudinger and Morrey–Sobolev inequalities (2009, background): “In particular, on the affine Lp isoperimetric inequality [37] (see Campi & Gronchi [9] for an alternate proof) and on the solution of the normalized Lp Minkowski problem [40].”
- Star body valued valuations (2009, unknown): “[3], [5], [10], [24], [29], [31], [33], [37].”
- Moment-entropy inequalities (2004, methodology): “We shall use the following result of Lutwak and Zhang (1997) [see also Lutwak, Yang and Zhang (2000), as well as Campi and Gronchi (2002)]: If K is an originsymmetric convex body, then V ( ∗pK)V (K) ≤ c2,(6.6) with equality if and only if K is an ellipsoid.”
- An asymmetric affine Pólya–Szegö principle (2012, background): “This was accomplished for the symmetric L projection bodies by Lutwak, Yang, and Zhang [54] (see also Campi and Gronchi [10] for an independent approach): If K ∈ K o , then”
- Sharp affine Sobolev type inequalities via the $\Lp$ Busemann-Petty centroid inequality (2015, unknown): “A more recent proof was obtained in [7] using the technique of shadow systems.”
- 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]).”
- Concentration of mass on convex bodies (2006, background): “Lutwak, Yang and Zhang (see [26] and [15] for a different proof) have established the following Lq affine isoperimetric inequality.”
- Asymmetric affine Lp Sobolev inequalities (2009, background): “The (symmetric) Lp projection body ΠpK of K ∈ Kno , defined in [26], is ΠpK = 1 2 · Π+p K +p 1 2 · Π−p K. Lutwak, Yang, and Zhang [26] (see also Campi and Gronchi [5]) established an Lp extension of the Petty projection inequality for the (symmetric) Lp projection operator which forms the geometry b”