Orlicz centroid bodies

By Erwin Lutwak, Deane Yang, Gaoyong Zhang. 2010

303 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Pharmacology

View Paper: https://www.semanticscholar.org/paper/cff3ed177bb2da86183657a13c658b5051efeebd

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In Applied Mathematics

In Geometry and Topology

In Pharmacology

Citations in the corpus

The Dual Orlicz–Minkowski Problem (2017, methodology): “This new theory started from the works of Lutwak, Yang and Zhang [35, 36] and Ludwig [27], and was greatly pushed forward by Gardner, Hug and Weil [12] and independently by Xi, Jin and Leng [46], due to the discovery of the Orlicz addition of convex bodies.”
The dual Orlicz–Brunn–Minkowski theory ☆ (2014, methodology): “The Orlicz-Brunn-Minkowski theory for convex bodies was launched by Lutwak, Yang, and Zhang [30, 31] with affine isoperimetric inequalities for Orlicz centroid and projection bodies.”
Anisotropic fractional perimeters (2013, unknown): “In recent years, centroid bodies have found powerful extensions within the L Brunn Minkowski theory [26–28,30], the asymmetric L Brunn Minkowski theory [21, 23] and the Orlicz Brunn Minkowski theory [29].”
The Centro-Affine Hadwiger Theorem (2013, background): “ies strengthen and directly imply their classical predecessors. Recently, the next step in the evolution of the Brunn-Minkowski theory towards an Orlicz Brunn-Minkowski theory has been made (see e.g. [27,42,47,57,58]). The functionals Ωϕ from 2 Theorem 1.2 constitute far reaching generalizations of ”
Orlicz–John ellipsoids (2014, background): “Beginning with the ground-breaking articles of Lutwak, Yang, Zhang and Harbel [22,39,40], a more wide extension of the Lp Brunn–Minkowski theory, called the Orlicz Brunn–Minkowski theory, emerged out three years ago.”
Necessary subspace concentration conditions for the even dual Minkowski problem (2017, background): “al Minkowski problem as well as the logarithmic Minkowski problem. The cone-volume measure for convex bodies has been studied extensively over the last few years in many diﬀerent contexts, see, e.g., [4, 5, 10, 11, 12, 23, 25, 27, 28, 29, 30, 31, 34, 35, 39, 40, 41, 42, 43, 44, 47, 51, 55, 56]. One ”
Anisotropic fractional Sobolev norms (2013, unknown): “[10, 15–17,21– 25,29–32]).”
THE ORLICZ-BRUNN-MINKOWSKI THEORY: A GENERAL FRAMEWORK, ADDITIONS, AND INEQUALITIES (2013, methodology): “The Orlicz centroid body ΓφK of K is defined in [28] (actually for any star body K) by”
Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems (2016, unknown): “The SL ( n ) invariance of the cone volume measure makes the measure a useful notion in the geometry of normed spaces, see [12, 61, 62, 66, 67, 70].”
Minkowski valuations intertwining the special linear group (2012, result): “Recently, her results led to strengthenings and generalizations of several affine isoperimetric and Sobolev inequalities [27,28,47,48].”
Dual Orlicz-Brunn-Minkowski theory (2014, methodology): “Zhang proved that the answer for the Busemann–Petty problem is affirmative when n = 4 in [55].”
The p-capacitary Orlicz–Hadamard variational formula and Orlicz–Minkowski problems (2017, methodology): “The Orlicz additions were proposed by Gardner, Hug and Weil in [15] and independently by Xi, Jin and Leng in [43], in order to provide the foundation of the newly initiated Orlicz-Brunn-Minkowski theory for convex bodies (with respect to volume) starting from the works [33, 34] of Lutwak, Yang and Z”