The dual Orlicz-Minkowski problem for capillary hypersurfaces

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 ϕ(h)G(X), where X=∇ h+hν and G 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 t>0 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 c=1. A uniform strict monotonicity condition under rescaling ensures uniqueness for c=1 and convergence of the unnormalized flow in any C^k norm at an exponential rate. The problem considered here includes the capillary L_p-Minkowski and L_p dual Minkowski problems as special cases.

The capillary L_p dual Christoffel-Minkowski problem for 1<p<q≤ k+1 with 1≤ k≤ n
Guanghan Li, Mengliang Liu
arXiv29 Sep 2026PreprintarXiv licenceFull textAnalysis & PDEs Geometry & topologyarXiv
The capillary L_p dual Minkowski problem for p>q in higher dimensions
Ya Gao
arXiv16 Oct 2026PreprintCC BY 4.0Full textAnalysis & PDEs Geometry & topologyarXiv
Capillary L_p dual Minkowski flow
Jinrong Hu, Yingxiang Hu, Bo Yang
arXiv2 Nov 2026PreprintarXiv licenceFull textAnalysis & PDEs Geometry & topologyarXiv
Affine dual Minkowski problem for general measures
Cheng Zhang, Hailin Jin
arXiv17 Sep 2026PreprintarXiv licenceFull textGeometry & topologyarXiv
The exact number of nonconstant positive solutions to the planar isotropic L_p dual Minkowski problem
Guanyu Tao
arXiv30 Sep 2026PreprintarXiv licenceFull textAnalysis & PDEs Geometry & topologyarXiv

Cite

BibTeX RIS

BibTeX

@misc{gao2026dual,
  title = {{The dual Orlicz-Minkowski problem for capillary hypersurfaces}},
  author = {Ya Gao},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02674},
  eprint = {2611.02674},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02674},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - The dual Orlicz-Minkowski problem for capillary hypersurfaces
AU  - Ya Gao
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02674
UR  - https://arxiv.org/abs/2611.02674
AB  - 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 ϕ(h)G(X), where X=∇ h+hν and G 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 t>0 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 c=1. A uniform strict monotonicity condition under rescaling ensures uniqueness for c=1 and convergence of the unnormalized flow in any C^k norm at an exponential rate. The problem considered here includes the capillary L_p-Minkowski and L_p dual Minkowski problems as special cases.
ER  -

Abstract

Related

Cite