Subspace concentration of dual curvature measures of symmetric convex bodies

By K. Boroczky, Martin Henk, H. Pollehn. Journal of differential geometry, 2018

116 citations recorded by the source corpus.

We prove a tight subspace concentration inequality for the dual curvature measures of a symmetric convex body. © 2018 International Press of Boston, Inc. All Rights Reserved.

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/138e228f0bd3ef592a0aff619c17b4f99c2a9647

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In Applied Mathematics

1. Qi-Rui Li
2. Haodi Chen
3. Jian Lu
4. Yiming Zhao
5. Yan-nan Liu
6. Shibing Chen
7. Yong Huang
8. Dongmeng Xi

In Molecular Biology

1. Haodi Chen
2. Sudan Xing
3. Baocheng Zhu
4. Yiming Zhao
5. Qi-Rui Li
6. Deping Ye
7. Shibing Chen
8. Dongmeng Xi

Citations in the corpus

• Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems (2017, background): “n [9] and [29], the existence of weak solutions was proved when the inhomogeneous term is a non-negative measure not concentrated in any sub-spaces. For other related results, we refer the readers to [8, 10, 37] and the references therein. Let us state our first main result as follows. Theorem 1.1. L”
• A flow method for the dual Orlicz–Minkowski problem (2020, background): “(3) is the dual Minkowski problem, which was first introduced by [33] and then studied by [6, 14, 29, 31, 42, 64, 65].”
• The Minkowski problem in Gaussian probability space (2020, background): “The dual Minkowski problem, while still largely open, has been solved in the o-symmetric case when the associated index q satisfies q ∈ [0, n], see, for example [8, 11, 15, 35, 38, 49, 74, 75].”
• The dual Minkowski problem for negative indices (2017, background): “rt of the dual Minkowski problem when the given measure is even was given by the author in [48]. Independently and simultaneously, the same condition was presented by B¨oroczky, Henk & Pollehn in [7] and shown by them to be necessary. In the current work, we consider the dual Minkowski problem f”
• The Dual Orlicz–Minkowski Problem (2017, background): “s) to the dual Minkowski problem with q∈ (0,n) for even measure µ. For q<0, the existence and uniqueness of the solution to the dual Minkowski problem were given recently in [55] by Zhao. See also [3, 56] for more works on the dual curvature measure and the related dual Minkowski problem. It is o”
• 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.”