On the planar dual Minkowski problem

By Shibing Chen, Qi-Rui Li. Advances in Mathematics, 2018

67 citations recorded by the source corpus.

Abstract In this paper, we resolve the planar dual Minkowski problem, proposed by Huang et al. (2016) [31] for all positive indices without any symmetry assumption. More precisely, given any q > 0 , and function f on S 1 , bounded by two positive constants, we show that there exists a convex body Ω in the plane, containing the origin in its interior, whose dual curvature measure C ˜ q ( Ω , ⋅ ) has density f. In particular, if f is smooth, then ∂Ω is also smooth.

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/85638918f44bfc4109f649527add84547eda6927

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In Applied Mathematics

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

In Molecular Biology

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

Citations in the corpus

• 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].”
• 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.”
• 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].”