Orlicz projection bodies

By Erwin Lutwak, Deane Yang, Gaoyong Zhang. 2010

311 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/600b3d75d06c1a154aa887ee75f15da66efaa337

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In Applied Mathematics

In Astronomy and Astrophysics

In Mathematical Physics

Citations in the corpus

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.”
Minkowski valuations and generalized valuations (2015, unknown): “, [2, 11, 32, 44–46, 61]).”
Projection bodies in complex vector spaces (2011, background): “For additional information and recent results on projection bodies see, for example, [14, 19, 23, 33, 34, 35, 36, 43, 51].”
Valuations and Surface Area Measures (2014, unknown): “[16,25,31,32]).”
Dual Orlicz–Brunn–Minkowski theory: Dual Orlicz Lϕ affine and geominimal surface areas (2014, methodology): “The Orlicz-Brunn-Minkowski theory for convex bodies, initiated from the work [29, 30] by Lutwak, Yang and Zhang, is the next generation of the Lp Brunn-Minkowski theory for convex bodies.”
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.”
OPERATIONS BETWEEN SETS IN GEOMETRY (2012, result): “Rather than elaborate on this in detail here, we mention only that some of the results are applied in [17] to further the new Orlicz-Brunn-Minkowski theory (see [35], [36]).”
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”
Stronger versions of the Orlicz-Petty projection inequality (2011, methodology): “ne the L 1polar projection body 1 to be K\( K). Unlike K, the Orlicz projection body ’Kis not translation invariant for a general ’2C, and may not be o-symmetric. However E. Lutwak, D. Yang, G. Zhang [34] show that ’AK= A ’Kholds for any A2GL(n), K2Kn o and ’2C: (4) The following Orlicz-Petty projec”
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 ”
The even Orlicz-Minkowski problem (2010, background): “This is the third paper in a series ([45], [46]) that attempts to develop some of the elements of an Orlicz Brunn-Minkowski theory.”
THE ORLICZ-BRUNN-MINKOWSKI THEORY: A GENERAL FRAMEWORK, ADDITIONS, AND INEQUALITIES (2013, methodology): “(Lutwak, Yang, and Zhang [29].)”