The planar Orlicz Minkowski problem in the \(L^1\)-sense

DOI10.1016/j.aim.2015.03.032zbMath1325.34057OpenAlexW1140134367WikidataQ112880098 ScholiaQ112880098MaRDI QIDQ2354397

Long Yiming, Sun Yijing

Publication date: 13 July 2015

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

Full work available at URL: https://doi.org/10.1016/j.aim.2015.03.032

zbMATH Keywords

variational methodMinkowski problemnegative powers

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Inequalities and extremum problems involving convexity in convex geometry (52A40) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50)

Related Items (19)

On the 2-dimensional dual Minkowski problem ⋮ Kirchhoff type equations with strong singularities ⋮ Mirror symmetric solutions to the centro-affine Minkowski problem ⋮ Multiple solutions of the planar \(L_p\) dual Minkowski problem ⋮ Orlicz-Aleksandrov-Fenchel inequality for Orlicz multiple mixed volumes ⋮ Existence and uniqueness of solutions to the Orlicz Aleksandrov problem ⋮ On a planar conformal curvature problem ⋮ Deforming a convex hypersurface by anisotropic curvature flows ⋮ Variational analysis of the planar \(L_p\) dual Minkowski problem ⋮ On the general dual Orlicz-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 ⋮ The dual Orlicz-Minkowski problem ⋮ Orlicz-Minkowski flows ⋮ Existence and uniqueness of solutions to Orlicz Minkowski problems involving \(0 < p < 1\) ⋮ The Orlicz Minkowski problem involving \(0 < p < 1 \): from one constant to an infinite interval ⋮ Variational characterization for the planar dual Minkowski problem ⋮ The planar Orlicz Minkowski problem for \(p=0\) without even assumptions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The two dimensional \(L_p\) Minkowski problem and nonlinear equations with negative exponents
• On the Orlicz Minkowski problem for polytopes
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• An exact estimate result for a class of singular equations with critical exponents
• An asymmetric affine Pólya-Szegő principle
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• Orlicz centroid bodies
• General affine surface areas
• The even Orlicz Minkowski problem
• General \(L_{p}\) affine isoperimetric inequalities
• Orlicz projection bodies
• Evolving plane curves by curvature in relative geometries. II
• Blaschke-Santaló inequalities
• The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation
• On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem.
• On the \(p\)-affine surface area
• The discrete planar \(L_0\)-Minkowski problem
• A generalized affine isoperimetric inequality
• Surface bodies and \(p\)-affine surface area
• On the Christoffel-Minkowski problem of Firey's \(p\)-sum
• On the regularity of solutions to a generalization of the Minkowski problem
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• A flow approach to the \(L_{-2}\) Minkowski problem
• The logarithmic Minkowski problem for polytopes
• Remarks on a planar conformal curvature problem
• \(L_p\) Minkowski problem with not necessarily positive data
• Asymmetric affine \(L_p\) Sobolev inequalities
• The role of the power 3 for elliptic equations with negative exponents
• On the \(L_{p}\) Minkowski problem for polytopes
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• On the regularity of the solution of then-dimensional Minkowski problem
• Classification of limiting shapes for isotropic curve flows
• On the $L_{p}$-Minkowski problem
• The logarithmic Minkowski problem
• Remarks on the 2-Dimensional L_p-Minkowski Problem
• Compatibility phenomena in singular problems
• Optimal Sobolev norms and the Lp Minkowski problem
• The Weyl and Minkowski problems in differential geometry in the large
• Self-similar solutions for the anisotropic affine curve shortening problem

This page was built for publication: The planar Orlicz Minkowski problem in the \(L^1\)-sense