The Orlicz version of the \(L_p\) Minkowski problem for \(- n < p < 0\)

DOI10.1016/j.aam.2019.101937zbMath1428.52009arXiv1812.05213OpenAlexW2904858820MaRDI QIDQ2334525

Gabriele Bianchi, Andrea Colesanti, Károly jun. Böröczky

Publication date: 7 November 2019

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

Full work available at URL: https://arxiv.org/abs/1812.05213

zbMATH Keywords

Monge-Ampère equation\(L_p\) Minkowski problemOrlicz Minkowski problem

Mathematics Subject Classification ID

Length, area, volume and convex sets (aspects of convex geometry) (52A38) Monge-Ampère equations (35J96)

Related Items

Smooth solutions to the Gauss image problem, The \(L_p\) Gauss image problem, Flow by 𝜎_{𝑘} curvature to the Orlicz Christoffel-Minkowski problem, On the discrete Orlicz electrostatic \(q\)-capacitary Minkowski problem, A \(L_p\) Brunn-Minkowski theory for logarithmic capacity, Orlicz-Minkowski flows, The \(L_p\) electrostatic \(q\)-capacitary Minkowski problem for general measures, The \(L_p\) Minkowski problem for torsion, Existence of smooth even solutions to the dual Orlicz-Minkowski problem, The L_p Minkowski problem for q-capacity

Cites Work

• Unnamed Item
• Mirror symmetric solutions to the centro-affine Minkowski problem
• On the Orlicz Minkowski problem for polytopes
• The Minkowski problem for polytopes
• Extremum problems for the cone volume functional of convex polytopes
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• The even Orlicz Minkowski problem
• General \(L_{p}\) affine isoperimetric inequalities
• Affine Moser-Trudinger and Morrey-Sobolev inequalities
• On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem.
• The \(L^p\)-Busemann-Petty centroid inequality
• The discrete planar \(L_0\)-Minkowski problem
• \(L_ p\) affine isoperimetric inequalities.
• The \(L_{p}\)-Minkowski problem for \(-n < p < 1\)
• General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. I
• Existence of solutions to the Orlicz-Minkowski problem
• The dual Orlicz-Minkowski problem
• \(L_{p}\) dual curvature measures
• Convex hypersurfaces of prescribed curvatures
• On the regularity of solutions to a generalization of the Minkowski problem
• On the regularity of the \(L_p\) Minkowski problem
• Rotationally symmetric solutions to the \(L_p\)-Minkowski problem
• A flow approach to the \(L_{-2}\) Minkowski problem
• On the \(L_{p}\) Monge-Ampère equation
• The logarithmic Minkowski problem for polytopes
• The \(L_p\) Minkowski problem for polytopes for \(0 < p < 1\)
• \(L_p\) Minkowski problem with not necessarily positive data
• Cone-volume measures of polytopes
• On the \(L_{p}\) Minkowski problem for polytopes
• Volume inequalities for subspaces of \(L_p\)
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• The centro-affine Minkowski problem for polytopes
• Continuity of the solution to the $L_{p}$ Minkowski problem
• Centro-Affine Invariants for Smooth Convex Bodies
• On the Discrete FunctionalL_pMinkowski Problem
• Deforming a hypersurface by its Gauss-Kronecker curvature
• On the regularity of the solution of then-dimensional Minkowski problem
• The logarithmic Minkowski problem for non-symmetric measures
• On the $L_{p}$-Minkowski problem
• The logarithmic Minkowski problem
• Remarks on the 2-Dimensional L_p-Minkowski Problem
• Infinitely Many Solutions for Centro-affine Minkowski Problem
• The Lp Minkowski problem for polytopes for p<0
• Convex Bodies The Brunn-MinkowskiTheory
• The Weyl and Minkowski problems in differential geometry in the large