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Capillary Lp dual Minkowski flow
Abstract
For n≥2 and θ∈(0,π/2), we study the long-time existence and asymptotic behavior of an even normalized capillary Lp dual Minkowski flow in the Euclidean half-space ℝn+1+̅. When pq≥0, the flow exists for all positive time and the evolving hypersurfaces converge smoothly along a sequence of times tending to infinity to a stationary solution of the normalized problem. If p≠ q, a dilation of the limit solves the unnormalized problem.
Related
- The capillary Lp dual Christoffel-Minkowski problem for 1<p<q≤ k+1 with 1≤ k≤ n
- The capillary Lp dual Minkowski problem for p>q in higher dimensions
- The dual Orlicz-Minkowski problem for capillary hypersurfaces
- Affine dual Minkowski problem for general measures
- The exact number of nonconstant positive solutions to the planar isotropic Lp dual Minkowski problem
BibTeX
@misc{hu2026capillary,
title = {{Capillary $L_p$ dual Minkowski flow}},
author = {Jinrong Hu and Yingxiang Hu and Bo Yang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02732},
eprint = {2611.02732},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02732},
}
RIS
TY - UNPB
TI - Capillary L_p dual Minkowski flow
AU - Jinrong Hu
AU - Yingxiang Hu
AU - Bo Yang
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02732
UR - https://arxiv.org/abs/2611.02732
AB - For n≥2 and θ∈(0,π/2), we study the long-time existence and asymptotic behavior of an even normalized capillary L_p dual Minkowski flow in the Euclidean half-space ℝ^n+1_+̅. When pq≥0, the flow exists for all positive time and the evolving hypersurfaces converge smoothly along a sequence of times tending to infinity to a stationary solution of the normalized problem. If p≠ q, a dilation of the limit solves the unnormalized problem.
ER -