Paper · Nov 2, 2026

The dual Orlicz-Minkowski problem for capillary hypersurfaces

Ya Gao

math.APWider flowsarXiv:2611.02674
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Abstract

We study curvature flows for the dual Orlicz–Minkowski problem for strictly convex capillary hypersurfaces in the Euclidean half-space. The prescribed function has the form , where and may be nonradial and nonhomogeneous. For acute contact angles, the evenness assumption together with either of the two integral conditions yields a smooth weighted-volume-preserving flow for all and a smooth solution to the dual Orlicz–Minkowski equation. Without the evenness assumption, two strict spherical-cap barriers yield the same conclusions for an unnormalized flow, whose limiting hypersurfaces solve the dual Orlicz–Minkowski equation with . A uniform strict monotonicity condition under rescaling ensures uniqueness for and convergence of the unnormalized flow in any norm at an exponential rate. The problem considered here includes the capillary -Minkowski and dual Minkowski problems as special cases.

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Submitted
Nov 2, 2026
Subjects
math.AP, math.DG
Other curvature flowsGauss curvature flowVolume-preserving & constrained flowsHomogeneous spacesStability & uniquenessFree boundary & capillary

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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.

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    Xinqun Mei, Guofang Wang and Liangjun WengWider flows

    Topics Gauss curvature flow, Free boundary & capillary, Other curvature flows · Shared terms “acute contact”, “capillary hypersurfaces”, “convex capillary”

  2. Capillary Orlicz-Minkowski flow in the upper half-space

    Guanghan Li and Chenyang LiuWider flows

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

  3. A class of anisotropic inverse Gauss curvature flows and dual Orlicz Minkowski type problem

    Shanwei Ding and Guanghan LiWider flows

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

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

    Shanwei Ding and Guanghan LiWider flows

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

  5. Inverse Gauss curvature flow in a time cone of Lorentz-Minkowski space

    Ya Gao and Jing MaoWider flows

    Topics Gauss curvature flow, Free boundary & capillary, Other curvature flows · Same author Ya Gao · Shared terms “Minkowski”, “rescaling”

  6. Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary

    Guofang Wang, Liangjun Weng and Chao XiaWider flows

    Topics Free boundary & capillary, Volume-preserving & constrained flows, Other curvature flows · Shared terms “capillary hypersurfaces”, “half space”, “convex capillary”

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

    Xia Zhao and Peibiao ZhaoWider flows

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

  8. A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space

    Yingxiang Hu, Yong Wei, Bo Yang et al.Wider flows

    Topics Free boundary & capillary, Volume-preserving & constrained flows, Other curvature flows · Shared terms “capillary hypersurfaces”, “convex capillary”, “half space”

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) Volume-preserving & constrained flows Wider flows Curvature flows with a constraint: subtract the average of the mean curvature and the enclosed volume stays fixed while area decreases, so spheres… Start with: On an area-preserving evolution equation for plane curves (Gage, 1986) Homogeneous spaces On homogeneous spaces Ricci flow reduces to an ordinary differential equation on a finite-dimensional space of invariant metrics. Start with: Ricci flow of locally homogeneous geometries on closed manifolds (Isenberg et al., 1992)

In the guidebook

  1. 11A.13
    Homogeneous FlowsBook 11A · The Ricci Flow: Existence and Maximum Principles

    A computable laboratory: the flow on Thurston’s geometries.