Paper · Oct 1, 2025

The chord Minkowski problem for super-critical exponent

Shibing Chen, Qi-Rui Li, Yuanyuan Li

math.APWider flowsarXiv:2510.01084
View PDF View HTML arXiv page

As on arXiv

Abstract

The chord Minkowski problem was recently introduced by Lutwak, Xi, Yang and Zhang, which seeks to determine the necessary and sufficient conditions for a given finite Borel measure such that it is the chord measure of a convex body. In this paper, we solve the chord Minkowski problem for the super-critical exponents by combining a nonlocal Gauss curvature flow introduced in and a topological argument developed in. Notably, we provide a simplified argument for the topological part.

View PDF View HTML arXiv page
Submitted
Oct 1, 2025
Subjects
math.AP

Comments: 22 pages

Other curvature flowsGauss curvature flow

Its neighbourhood

Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Uniqueness of solutions to the logarithmic Minkowski problem in ℝ³ (Shibing Chen, Yibin Feng and Weiru Liu, 2022)5Chen 2022 Smooth solutions to the chord log-Minkowski problem (Jinrong Hu, Yong Huang and Jian Lu, 2023)4Hu 2023 The chord Gauss curvature flow and its Lₚ chord Minkowski problem (Jinrong Hu, Yong Huang, Jian Lu et al., 2023)1Hu 2023 Flow by Gauss Curvature to the orlicz Chord Minkowski Problem (Xia Zhao and Peibiao Zhao, 2023)3Zhao 2023 Flow by Gauss curvature to the Minkowski problem of p-harmonic measure (Chao Li and Xia Zhao, 2024)6Li 2024 Gauss curvature flow to the Lₚ-Gaussian chord Minkowski problem (Xia Zhao and Peibiao Zhao, 2024)2Zhao 2024 Regularity of the p-Gauss curvature flow with flat side (Genggeng Huang, Xu-Jia Wang and Yang Zhou, 2024)8Huang 2024 The Lₚ Gauss dual Minkowski problem (Na Fu and Jianping Sun, 2024)7Fu 2024
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. The chord Gauss curvature flow and its chord Minkowski problem

    Jinrong Hu, Yong Huang, Jian Lu et al.Wider flows

    Topics Gauss curvature flow, Other curvature flows · Shared terms “chord Minkowski”, “nonlocal Gauss”

  2. Gauss curvature flow to the -Gaussian chord Minkowski problem

    Xia Zhao and Peibiao ZhaoWider flows

    Topics Gauss curvature flow, Other curvature flows · Shared terms “chord Minkowski”, “chord measure”

  3. Flow by Gauss Curvature to the orlicz Chord Minkowski Problem

    Xia Zhao and Peibiao ZhaoWider flows

    Topics Gauss curvature flow, Other curvature flows · Shared terms “chord Minkowski”, “chord measure”, “Lutwak”

  4. Smooth solutions to the chord log-Minkowski problem

    Jinrong Hu, Yong Huang and Jian LuWider flows

    Topics Gauss curvature flow, Other curvature flows · Shared terms “Minkowski”, “nonlocal Gauss”, “chord measure”

  5. Uniqueness of solutions to the logarithmic Minkowski problem in

    Shibing Chen, Yibin Feng and Weiru LiuWider flows

    Topics Gauss curvature flow, Other curvature flows · Same author Shibing Chen · Shared terms “Minkowski”

  6. Flow by Gauss curvature to the Minkowski problem of p-harmonic measure

    Chao Li and Xia ZhaoWider flows

    Topics Gauss curvature flow, Other curvature flows · Shared terms “Minkowski”

  7. The Gauss dual Minkowski problem

    Na Fu and Jianping SunWider flows

    Topics Gauss curvature flow, Other curvature flows · Shared terms “convex body”, “Borel measure”, “finite Borel”

  8. Regularity of the -Gauss curvature flow with flat side

    Genggeng Huang, Xu-Jia Wang and Yang ZhouWider flows

    Topics Gauss curvature flow, Other curvature flows

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Other curvature flows Wider flows Flows that move a hypersurface or metric by some other function of curvature: Gauss curvature (worn stones), inverse mean curvature (the Penrose… Start with: Shapes of worn stones (Firey, 1974) Gauss curvature flow Wider flows Convex hypersurfaces shrink with normal speed a power K^α of their Gauss curvature. Firey proposed it as a model of stones worn by waves; for α>… Start with: Shapes of worn stones (Firey, 1974)