The logarithmic Minkowski problem for non-symmetric measures

By Shibing Chen, Qi-Rui Li, Guangxian Zhu. Transactions of the American Mathematical Society, 2018

126 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0613d22d71e135d2d5380dd1e1b0462f9c382a42

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. Qi-Rui Li
3. Haodi Chen
4. Shibing Chen
5. K. Boroczky
6. Deane Yang
7. Yong Huang
8. Gaoyong Zhang

In Mathematical Physics

1. Yiming Zhao
2. K. Boroczky
3. Gaoyong Zhang
4. Deane Yang
5. Erwin Lutwak
6. Haodi Chen
7. Qi-Rui Li
8. Deping Ye

Citations in the corpus

• Variations of a class of Monge–Ampère-type functionals and their applications (2021, methodology): “[4, 7, 16, 17, 19, 21, 30, 32] for the Lp-Minkowski problem, and [5, 15, 24, 25, 29, 38] for the dual Minkowski problem.”
• The dual Minkowski problem for symmetric convex bodies (2017, background): “ely open (see B¨oro¨czky-LutwakYang-Zhang [9], Huang-Liu-Xu [28], Jian-Lu-Wang [32], and Zhu [55,57]). For other recent progress on the Lp-Minkowski problem, see B¨oro¨czky-Trinh [11] and Chen-Li-Zhu [12,13]. The Lp Minkowski problem also plays a key role in establishing affine Sobolev inequalities (s”
• The Lp dual Minkowski problem and related parabolic flows (2021, background): “Since when q = n + 1, it becomes the Lp-Minkowski problem which has been extensively studied by many authors [6, 7, 10, 22, 21, 25, 31, 36, 40] (see also the references therein), in our first main theorem below we deals with the case q 6= n+ 1.”
• A flow method for the dual Orlicz–Minkowski problem (2020, background): “[5, 7, 8, 15, 17, 28, 32, 36, 39, 40, 41, 47, 48, 49, 50, 52, 54, 67, 68] and Schneider’s book [59], and corresponding references therein.”
• Necessary subspace concentration conditions for the even dual Minkowski problem (2017, background): “ass is at the origin, was given in the discrete case by Henk and Linke [29], and in the general setting by B¨oro¨czky and Henk [7]. For a related stability result concerning (1.8) we refer to [8]. In [15], Chen, Li and Zhu proved that also in the non-symmetric logarithmic Minkowski problem the subsp”
• The L dual Minkowski problem for p > 1 and q > 0 (2018, unknown): “here is positive. In addition, if −n < p ≤ 0 and f is any non-negative L n n+p function on Sn−1 such that R Sn−1 f dµ > 0, then (12) has a solution, where the case p = 0 is due to Chen, Li, Zhu [10], and the case p ∈ (−n,0) is due to Bianchi, B¨oro¨czky, Colesanti, Yang [4]. We also note that ”