The \(L_p\) Minkowski problem for the electrostatic \(\mathfrak{p}\)-capacity

DOI10.4310/jdg/1606964418zbMath1453.31012OpenAlexW3109937143WikidataQ115164594 ScholiaQ115164594MaRDI QIDQ2213950

Ge Xiong, Zou Du

Publication date: 4 December 2020

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jdg/1606964418

zbMATH Keywords

convex bodyBrunn-Minkowski theoryMinkowski problem\(p\)-capacity

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items

The Orlicz Minkowski problem for the electrostatic \(\mathfrak{p}\)-capacity ⋮ Symmetry results for overdetermined problems via \(L_p\) Brunn-Minkowski inequalities ⋮ The discrete Orlicz-Minkowski problem for \(p\)-capacity ⋮ The uniqueness of the \(L_p\) Minkowski problem for \(q\)-torsional rigidity ⋮ The equality cases in Steiner's projection inequality ⋮ The discrete logarithmic Minkowski problem for \(q\)-capacity ⋮ On the existence of solutions to the Orlicz Aleksandrov problem ⋮ On the \(L_p\) Gaussian Minkowski problem ⋮ The functional Orlicz–Brunn–Minkowski inequality for q‐torsional rigidity ⋮ A curvature flow to the \(L_p\) Minkowski-type problem of \(q\)-capacity ⋮ On the polar Orlicz Minkowski type problem for the general mixed \(\mathfrak{p}\)-capacity ⋮ A flow to the Orlicz-Minkowski-type problem of \(\mathfrak{p}\)-capacity ⋮ On the existence of solutions to the Orlicz-Minkowski problem for torsional rigidity ⋮ On the discrete Orlicz electrostatic \(q\)-capacitary Minkowski problem ⋮ A \(L_p\) Brunn-Minkowski theory for logarithmic capacity ⋮ Sharp affine isoperimetric inequalities for the volume decomposition functionals of polytopes ⋮ The \(L_p\) electrostatic \(q\)-capacitary Minkowski problem for general measures ⋮ The \(L_p\) Minkowski problem for torsion ⋮ The functional form of the dual mixed volume ⋮ On the continuity of the solutions to the $L_p$ capacitary Minkowski problem ⋮ On the Orlicz Minkowski problem for logarithmic capacity ⋮ The L_p Minkowski problem for q-capacity ⋮ The L_p Minkowski problem for the electrostatic p-capacity for $p\ge n$ ⋮ Uniqueness of solutions to the logarithmic Minkowski problem in \(\mathbb{R}^3\) ⋮ The logarithmic capacitary Minkowski problem for polytopes

Cites Work

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• Operations between sets in geometry
• Orlicz-John ellipsoids
• The Brunn-Minkowski-Firey inequality for nonconvex sets
• The log-Brunn-Minkowski inequality
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• Brunn-Minkowski inequalities for variational functionals and related problems
• The Minkowski problem for 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
• Capacitary inequalities of the Brunn-Minkowski type
• The Hadamard variational formula and the Minkowski problem for \(p\)-capacity
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
• A volume inequality for polar bodies
• General affine surface areas
• The even Orlicz Minkowski problem
• Capacities, surface area, and radial sums
• General \(L_{p}\) affine isoperimetric inequalities
• Affine Moser-Trudinger and Morrey-Sobolev inequalities
• A Minkowski problem for electrostatic capacity
• Blaschke-Santaló inequalities
• The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation
• Ellipsoids and matrix-valued valuations
• The Brunn-Minkowski inequality for \(p\)-capacity of convex bodies
• A new ellipsoid associated with convex bodies
• The \(L^p\)-Busemann-Petty centroid inequality
• The discrete planar \(L_0\)-Minkowski problem
• The affine Sobolev inequality.
• \(L_ p\) affine isoperimetric inequalities.
• A unified treatment for \(L_p\) Brunn-Minkowski type inequalities
• A probabilistic approach to the geometry of the \(\ell^n_p\)-ball
• Sharp affine \(L_ p\) Sobolev inequalities.
• Gauss curvature flow: The fate of the rolling stones
• The Cramer-Rao inequality for star bodies
• Convex hypersurfaces of prescribed curvatures
• On the Christoffel-Minkowski problem of Firey's \(p\)-sum
• On the case of equality in the Brunn-Minkowski inequality for capacity
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Rotationally symmetric solutions to the \(L_p\)-Minkowski problem
• 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
• Asymmetric affine \(L_p\) Sobolev inequalities
• The minimal Orlicz surface area
• 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
• Orlicz-Legendre ellipsoids
• Relative entropy of cone measures and L _p centroid bodies
• The surface measure and cone measure on the sphere of ℓ_{𝑝}ⁿ
• Some regularity properties of solutions of Monge Ampère equation
• Shapes of worn stones
• On the regularity of the solution of then-dimensional Minkowski problem
• The Brunn-Minkowski inequality
• Convex Bodies with Identical John and LYZ Ellipsoids
• $L_p$ John Ellipsoids
• On the $L_{p}$-Minkowski problem
• The logarithmic Minkowski problem
• Remarks on the 2-Dimensional L_p-Minkowski Problem
• Convex and Discrete Geometry
• Convex Bodies The Brunn-MinkowskiTheory
• Optimal Sobolev norms and the Lp Minkowski problem
• $p$-Means of Convex Bodies.
• The Weyl and Minkowski problems in differential geometry in the large