The Christoffel problem in the hyperbolic plane

DOI10.1016/J.AAM.2023.102557zbMath1527.34069OpenAlexW4380368240MaRDI QIDQ6170333

Yao Wan, Haizhong Li

Publication date: 12 July 2023

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2023.102557

zbMATH Keywords

hyperbolic planeChristoffel problemgeneralized Blaschke-Santaló inequalityhorospherical \(p\)-Minkowski problem

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Periodic solutions to ordinary differential equations (34C25) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Cites Work

• The two dimensional \(L_p\) Minkowski problem and nonlinear equations with negative exponents
• \(2\pi\)-periodic self-similar solutions for the anisotropic affine curve shortening problem. II
• 2\(\pi\)-periodic self-similar solutions for the anisotropic affine curve shortening problem
• Multiple solutions of the planar \(L_p\) dual Minkowski problem
• Hypersurfaces in \(\mathbb H^{n+1}\) and conformally invariant equations: the generalized Christoffel and Nirenberg problems
• On solvability of two-dimensional \(L_{p}\)-Minkowski problem.
• A generalized affine isoperimetric inequality
• Volume preserving flow and Alexandrov-Fenchel type inequalities in hyperbolic space
• \(L_p\) Minkowski problem with not necessarily positive data
• Lorentzian area measures and the Christoffel problem
• Remarks on the 2-Dimensional L_p-Minkowski Problem
• The determination of convex bodies from their mean radius of curvature functions
• Christoffel's problem for general convex bodies
• Existence of Self-similar Solutions to the Anisotropic Affine Curve-shortening Flow
• Self-similar solutions for the anisotropic affine curve shortening problem

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