The Lp Minkowski problem for polytopes for 0 < p < 1

By Guangxian Zhu. 2014

149 citations recorded by the source corpus.

Necessary and sufficient conditions are given for the existence of solutions to the discrete Lp Minkowski problem for the critical case where 0 < p < 1.

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/f738ad0f4a0657938673e6e2130ea583a3fdd9c3

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In Applied Mathematics

In Molecular Biology

Citations in the corpus

The Dual Orlicz–Minkowski Problem (2017, background): “ent back to Minkowski [37, 38]. The Lp Minkowski problem was ﬁrst posed by Lutwak [30]. Since then, the Lp Minkowski problem attracted a lot of attention and amazing progress has been made (see e.g., [5, 6, 18, 21, 22, 33, 45, 61, 62, 63]). When p= 0, it becomes the logarithmic Minkowski problem (se”
Existence of solutions to the even dual Minkowski problem (2018, background): “In the general case (noneven case), different efforts have been made by Böröczky, Hegedűs & Zhu [5], Stancu [61, 62], and Zhu [70].”
The dual Minkowski problem for symmetric convex bodies (2017, background): “general case. Alternate proofs were given by Hug-Lutwak-Yang-Zhang [31]. The case of p < 1 is still largely 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-”
On the L dual Minkowski problem (2018, methodology): “See also Jian, Lu & Zhu [37], Lu & Wang [41], Zhu [71], etc., on this problem.”
Necessary subspace concentration conditions for the even dual Minkowski problem (2017, background): “ be the conevolume measure VK(·) of a convex body K ∈ Kn o. This is the p = 0 limit case of the general Lp-Minkowski problem within the above mentioned Lp Brunn-Minkowski theory for which we refer to [32, 38, 57] and the references within. The discrete, planar, even case of the logarithmic Minkowski”
An extension of Minkowski's theorem and its applications to questions about projections for measures (2016, methodology): “ developing Brunn-Minkowski-Firey theory (see more in Ludwig [40], Lutwak [41], [42], Lutwak, Yang, Zhang [45], [46], [47], Lutwak, Oliker [44], Meyer, Werner [50], Ryabogin, Zvavitch [55], Zhu [63], [64], and the references therein). In this manuscript, we prove an analogue of Minkowski’s theorem i”
The dual Minkowski problem for negative indices (2017, background): “Böröczky, Hegedűs, & Zhu [5] later found a sufficient condition for the discrete case, which includes [9] (in the discrete case) and [49] as special cases.”