The logarithmic Minkowski problem for polytopes

By Guangxian Zhu. 2014

264 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0ee049a585989010635c583f4fe01b26dfdd5033

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. Yong Huang
3. Deping Ye
4. Qi-Rui Li
5. Shibing Chen
6. K. Boroczky
7. Deane Yang
8. Sudan Xing

In Geometry and Topology

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

Citations in the corpus

• The discrete logarithmic Minkowski problem (2014, methodology): “[67] G. Zhu, The centro-affine Minkowski problem for polytopes.”
• Cone-volume measure of general centered convex bodies (2016, unknown): “Zhu [45,46], K.”
• The Lp Minkowski problem for polytopes for 0 < p < 1 (2014, unknown): “cently established by B¨oro¨czky, et al. [5]. Without the assumption that the measure is even, existence of solution of the PDE (1.1) for the case where p &gt; −n were given by Chou and Wang [10]. In [59,60], the author established necessary and sufficient conditions for the existence of the solution ”
• On the L dual Minkowski problem (2018, background): “See also Jian, Lu & Zhu [37], Lu & Wang [41], Zhu [71], etc., on this problem.”
• Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems (2016, background): “The case of p=1 is the classical Minkowski problem, the case of p=0 is the logarithmic Minkowski problem (see [14]), and the case of p=−n is the centro-affine Minkowski problem (see Chou–Wang [20], Lu– Wang [46], and Zhu [83]).”
• An extension of Minkowski's theorem and its applications to questions about projections for measures (2016, background): “The Lp-Minkowski problem is one of the main questions in the rapidly developing Brunn-Minkowski-Firey theory (see more in Ludwig [39], Lutwak [40], [41], Lutwak, Yang, Zhang [44], [45], [46], Lutwak, Oliker [43], Meyer, Werner [49], Ryabogin, Zvavitch [54], Zhu [62], [63], and the references therein”
• On the planar dual Minkowski problem (2018, background): “The L0-Minkowski problem, also called the logarithmic Minkowski problem [7, 10, 53], is highly interesting.”
• Existence of solutions to the even dual Minkowski problem (2018, background): “See also Jian, Lu & Zhu [35], Lu & Wang [36], Zhu [71], etc., on this problem.”
• The dual Minkowski problem for symmetric convex bodies (2017, methodology): “[57] G. Zhu, The Lp Minkowski problem for polytopes for 0 p 1, J. Funct.”
• Necessary subspace concentration conditions for the even dual Minkowski problem (2017, unknown): “In [15], Chen, Li and Zhu proved that also in the non-symmetric logarithmic Minkowski problem the subspace concentration condition is sufficient.”