On the \(L^p\) Aleksandrov problem for negative \(p\)

DOI10.1016/j.aim.2022.108573zbMath1497.52005OpenAlexW4285982386MaRDI QIDQ2172214

Stephanie Mui

Publication date: 15 September 2022

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

Full work available at URL: https://doi.org/10.1016/j.aim.2022.108573

zbMATH Keywords

\(L^p\) Aleksandrov problem\(L^p\) integral curvature

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Variational methods for second-order elliptic equations (35J20) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

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On the existence of solutions to the Orlicz Aleksandrov problem ⋮ On subspace concentration for dual curvature measures ⋮ The \(L_p\) chord Minkowski problem

Cites Work

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• Mirror symmetric solutions to the centro-affine Minkowski problem
• The log-Brunn-Minkowski inequality
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• Extremum problems for the cone volume functional of convex polytopes
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• Cone-volume measure of general centered convex bodies
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• 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 affine Sobolev inequality.
• \(L_ p\) affine isoperimetric inequalities.
• Existence of solutions to the even dual Minkowski problem
• General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. I
• On the \(L_p\) dual Minkowski problem
• Subspace concentration of dual curvature measures of symmetric convex bodies
• The \(L_p\)-Aleksandrov problem for \(L_p\)-integral curvature
• Necessary subspace concentration conditions for the even dual Minkowski problem
• The \(L_{p}\) dual Minkowski problem for \(p\) 1 and \(q\) 0
• \(L_{p}\) dual curvature measures
• Sharp affine \(L_ p\) Sobolev inequalities.
• Projecting the surface measure of the sphere of \({\ell}_p^n\)
• Rotationally symmetric solutions to the \(L_p\)-Minkowski problem
• On the \(L_{p}\) Monge-Ampère equation
• Sharp Sobolev inequalities via projection averages
• The logarithmic Minkowski problem for polytopes
• Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems
• The dual Minkowski problem for symmetric convex bodies
• \(L_p\) Minkowski problem with not necessarily positive data
• Embedding \(\mathbb S^n\) into \(\mathbb R^{n+1}\) with given integral Gauss curvature and optimal mass transport on \(\mathbb S^n\)
• Asymmetric affine \(L_p\) Sobolev inequalities
• Smooth solutions to the \(L_p\) dual Minkowski problem
• Cone-volume measures of polytopes
• On the \(L_{p}\) Minkowski problem for polytopes
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• The centro-affine Minkowski problem for polytopes
• On the Discrete Logarithmic Minkowski Problem
• Curvature Measures
• The Gauss Image Problem
• On the regularity of the solution of then-dimensional Minkowski problem
• The logarithmic Minkowski problem for non-symmetric measures
• The logarithmic Minkowski problem
• Hypersurfaces in IRⁿ⁺¹with prescribed gaussian curvature and related equations of monge—ampére type
• The 𝐿_{𝑝} Aleksandrov problem for origin-symmetric polytopes
• Convex and Discrete Geometry
• Convex Bodies The Brunn-MinkowskiTheory
• Optimal Sobolev norms and the Lp Minkowski problem
• The Weyl and Minkowski problems in differential geometry in the large

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