Topological degree method for the rotationally symmetric \(L_p\)-Minkowski problem

DOI10.3934/dcds.2016.36.971zbMath1326.35169OpenAlexW2339056752MaRDI QIDQ495805

Jian Lu, Huai-Yu Jian

Publication date: 15 September 2015

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2016.36.971

zbMATH Keywords

existence of solutionstopological degreeMonge-Ampère equationMinkowski problemcentro-affine Gauss curvature

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Affine differential geometry (53A15) Singular elliptic equations (35J75) Symmetries, invariants, etc. in context of PDEs (35B06) Monge-Ampère equations (35J96)

Related Items (6)

Mirror symmetric solutions to the centro-affine Minkowski problem ⋮ A generalized rotationally symmetric case of the centroaffine Minkowski problem ⋮ Existence of solutions to the Orlicz-Minkowski problem ⋮ A remark on rotationally symmetric solutions to the centroaffine Minkowski problem ⋮ A flow method for the dual Orlicz–Minkowski problem ⋮ Nonexistence of maximizers for the functional of the centroaffine Minkowski problem

Cites Work

• Unnamed Item
• Unnamed Item
• Bernstein theorem and regularity for a class of Monge-Ampère equations
• 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
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Evolving convex curves
• Axioms and fundamental equations of image processing
• The scalar curvature equation on 2- and 3-spheres
• Blaschke-Santaló inequalities
• On solvability of two-dimensional \(L_{p}\)-Minkowski problem.
• On positive scalar curvature on \(S^2\)
• Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
• Prescribed scalar curvature on the \(n\)-sphere
• Rotationally symmetric solutions to the \(L_p\)-Minkowski problem
• The logarithmic Minkowski problem for polytopes
• \(L_p\) Minkowski problem with not necessarily positive data
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• The centro-affine Minkowski problem for polytopes
• On the $L_{p}$-Minkowski problem
• A necessary and sufficient condition for the nirenberg problem
• The logarithmic Minkowski problem
• Self-similar solutions for the anisotropic affine curve shortening problem

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