Orlicz–John ellipsoids

By Du Zou, Ge Xiong. 2014

120 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0f6649ad508cb0235d82baa2749ccf3de45370e0

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

1. Yiming Zhao
2. Yan-nan Liu
3. Jian Lu
4. Yong Huang
5. Sudan Xing
6. Deping Ye
7. Baocheng Zhu
8. Dongmeng Xi

In Geometry and Topology

1. Yiming Zhao
2. Deping Ye
3. Sudan Xing
4. Dongmeng Xi
5. Baocheng Zhu
6. Ning Zhang
7. Hansol Hong
8. Yong Huang

Citations in the corpus

• On the L dual Minkowski problem (2018, background): “See, for example, Barthe, Guédon, Mendelson & Naor [4], Böröczky & Henk [7], Böröczky, Lutwak, Yang & Zhang [9–11], Henk & Linke [29], Ludwig [44], Ludwig & Reitzner [47], Naor [54], Naor & Romik [55], Paouris & Werner [56], Stancu [62,63], Xiong [65], Zhu [70], and Zou & Xiong [73].”
• The p-capacitary Orlicz–Hadamard variational formula and Orlicz–Minkowski problems (2017, methodology): “es (with respect to volume) starting from the works [33, 34] of Lutwak, Yang and Zhang. The Orlicz theory is in great demand (see e.g., [47] for some motivations) and is rapidly developing (see e.g., [4, 6, 19, 30, 42, 44, 45, 46, 53]). In particular, we establish the p-capacitary OrliczBrunn-Minkow”
• The Minkowski problem in Gaussian probability space (2020, result): “See also [22,36,40,48,71,78] for additional results and contributions in the Orlicz extension of the classical Brunn-Minkowski theory.”
• The dual Minkowski problem for negative indices (2017, background): “When p = 0, Lp surface area measure is best known as the cone volume measure and is being intensively studied, see, for example, Barthe, Guédon, Mendelson & Naor [4], Böröczky-LYZ [8–10], Böröczky & Henk [6], Henk & Linke [25], Ludwig & Reitzner [29], Stancu [42,43], Zhu [49], and Zou & Xiong [52].”
• The Dual Orlicz–Minkowski Problem (2017, methodology): “In particular, the Orlicz mixed volumes of convex bodies have been obtained in [12, 46], which were used to discover, for instance, the Orlicz affine and geominimal surface areas and the Orlicz-John ellipsoid [47, 50, 57, 64].”
• Existence of solutions to the even dual Minkowski problem (2018, background): “Naor [47], Naor & Romik [48], Paouris & Werner [51], Stancu [61, 62], Xiong [65], Zhu [70], and Zou & Xiong [74].”
• A flow method for the dual Orlicz–Minkowski problem (2020, background): “They have attracted great attention from many researchers, see for example [11, 20, 22, 27, 29, 30, 32, 33, 34, 36, 43, 45, 51, 53, 55, 56, 58, 60, 63, 66, 69] and references therein.”