Paper · Jan 21, 2026

Capillary Orlicz-Minkowski flow in the upper half-space

Guanghan Li, Chenyang Liu

math.DGWider flowsarXiv:2601.14659
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Abstract

In this paper, we study the long-time existence and asymptotic behavior of an anisotropic capillary Gauss curvature flow. By studying this flow and proving its convergence to a stationary solution, we establish a new existence result for the capillary Orlicz-Minkowski problem without the evenness assumption, and provide a flow approach to the existence of smooth solutions.

Other curvature flowsGauss curvature flowFree boundary & capillaryLong-time existence & convergence

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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 2021, 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 A Gauss curvature flow related to the Orlicz-Aleksandrov problem (Bin Chen and Peibiao Zhao, 2021)7Chen 2021 Anisotropic flows without global terms and dual Orlicz Christoffel-Minkowski type problem (Shanwei Ding and Guanghan Li, 2022)3Ding 2022 A class of anisotropic inverse Gauss curvature flows and dual Orlicz Minkowski type problem (Shanwei Ding and Guanghan Li, 2022)1Ding 2022 An inverse Gauss curvature flow and its application to p-capacitary Orlicz-Minkowski problem (Bin Chen, Weidong Wang, Xia Zhao et al., 2023)4Chen 2023 Flow by Gauss Curvature to the Orlicz Minkowski Problem for q-torsional rigidity (Xia Zhao and Peibiao Zhao, 2024)5Zhao 2024 The capillary Gauss curvature flow (Xinqun Mei, Guofang Wang and Liangjun Weng, 2025)6Mei 2025 Free boundary flows by powers of the Gauss curvature in the unit ball (Tianci Luo, Yong Wei and Rong Zhou, 2026)8Luo 2026 Uniqueness of capillary Gauss solitons (Xinqun Mei, Guofang Wang and Liangjun Weng, 2026)2Mei 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. A class of anisotropic inverse Gauss curvature flows and dual Orlicz Minkowski type problem

    Shanwei Ding and Guanghan LiWider flows PDF

    Topics Gauss curvature flow, Long-time existence & convergence, Other curvature flows · Same author Guanghan Li · Shared terms “Orlicz Minkowski”, “stationary solutions”, “asymptotic behavior”

  2. Uniqueness of capillary Gauss solitons

    Xinqun Mei, Guofang Wang and Liangjun WengWider flows PDF

    Topics Gauss curvature flow, Free boundary & capillary, Other curvature flows · Shared terms “half space”

  3. Anisotropic flows without global terms and dual Orlicz Christoffel-Minkowski type problem

    Shanwei Ding and Guanghan LiWider flows PDF

    Topics Gauss curvature flow, Long-time existence & convergence, Other curvature flows · Same author Guanghan Li · Shared terms “Orlicz”, “Minkowski”, “stationary solutions”

  4. An inverse Gauss curvature flow and its application to p-capacitary Orlicz-Minkowski problem

    Bin Chen, Weidong Wang, Xia Zhao et al.Wider flows PDF

    Topics Gauss curvature flow, Long-time existence & convergence, Other curvature flows · Shared terms “Orlicz Minkowski”, “smooth solutions”

  5. Flow by Gauss Curvature to the Orlicz Minkowski Problem for q-torsional rigidity

    Xia Zhao and Peibiao ZhaoWider flows PDF

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

  6. The capillary Gauss curvature flow

    Xinqun Mei, Guofang Wang and Liangjun WengWider flows PDF

    Topics Gauss curvature flow, Free boundary & capillary, Other curvature flows

  7. A Gauss curvature flow related to the Orlicz-Aleksandrov problem

    Bin Chen and Peibiao ZhaoWider flows PDF

    Topics Gauss curvature flow, Other curvature flows · Shared terms “Orlicz”, “smooth solutions”

  8. Free boundary flows by powers of the Gauss curvature in the unit ball

    Tianci Luo, Yong Wei and Rong ZhouWider flows PDF

    Topics Gauss curvature flow, Free boundary & capillary, Long-time existence & convergence · Shared terms “half space”

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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) Free boundary & capillary Flows whose boundary is free to slide on a support surface, meeting it at a right angle (free boundary) or at a fixed angle (capillary). Start with: Non-parametric mean curvature evolution with boundary conditions (Huisken, 1989) Long-time existence & convergence A geometric flow either runs forever or stops because something blows up. Extension criteria say which quantity must blow up at a finite singular… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982)