Projection problems for symmetric polytopes

By Binwu He, Gangsong Leng, Kanghai Li. 2006

81 citations recorded by the source corpus.

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/aaa8ff081deffb051bd2a7aae03d87cc6b848491

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In Applied Mathematics

1. Yiming Zhao
2. K. Boroczky
3. Deane Yang
4. Gaoyong Zhang
5. Erwin Lutwak
6. Deping Ye
7. Dongmeng Xi
8. Yong Huang

In Molecular Biology

1. Yiming Zhao
2. Deane Yang
3. Gaoyong Zhang
4. Erwin Lutwak
5. K. Boroczky
6. Dongmeng Xi
7. Martin Henk
8. Eva Linke

Citations in the corpus

• The logarithmic Minkowski problem (2012, unknown): “For origin-symmetric polytopes, the subspace concentration inequality of Theorem 5.2 was established previously by He, Leng and Li [28], with an alternate proof given by Xiong [62].”
• Cone-volume measure of general centered convex bodies (2016, unknown): “Li [22].”
• Affine images of isotropic measures (2015, background): “with equality if and only if K is a parallelotope? When K is an origin-symmetric polytope, He, Leng, and Li [30] established inequality (8.”
• Cone-volume measures of polytopes (2013, methodology): “3) was proven in the special case dimL = 1 by Hernández Cifre (2007, private communication), in the cases dimL = 1, n− 1 by Xiong [27], and for originsymmetric polytopes independently by Henk, Schürmann & Wills [14] and by He, Leng & Li [13].”
• 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 discrete logarithmic Minkowski problem (2014, unknown): “e-volume measure of this convex body satisfies the subspace concentration condition. For more references on the progress of the subspace concentration condition, see, e.g., Henk et al. [32], He et al. [30], Xiong [67], B¨oro¨czky et al. [8], and Henk and Linke [31]. In [6], B¨oro¨czky, et al. establi”
• Dar’s conjecture and the log–Brunn–Minkowski inequality (2016, background): “It was first proved by He, Leng, and Li [27] that the cone-volume measures of o-symmetric polytopes in R satisfy the subspace concentration inequality (2.”
• The logarithmic Minkowski problem for polytopes (2014, unknown): “In [6], Böröczky, Lutwak, Yang and Zhang (for polytopes see He, Leng and Li [31], and Xiong [71]) showed that if ξ is a subspace of R with 0 < dim ξ < n and μ is the cone-volume measure of an origin-symmetric convex body, then μ(ξ ∩ Sn−1) ≤ dim ξ n μ(Sn−1).”