The Lp Minkowski problem for q-capacity

DOI10.1017/prm.2020.57zbMath1469.31018OpenAlexW3088390710MaRDI QIDQ5001561

Zhengmao Chen

Publication date: 22 July 2021

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/prm.2020.57

zbMATH Keywords

\(L_p\) Minkowski inequality\(q\)-capacity\(L_p\) \(q\)-capacity measure

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 (2)

An isoperimetric inequality for the first Steklov-Dirichlet Laplacian eigenvalue of convex sets with a spherical hole ⋮ A reverse quantitative isoperimetric type inequality for the Dirichlet Laplacian

Cites Work

• The dual Minkowski problem for negative indices
• Brunn-Minkowski inequalities for variational functionals and related problems
• Interior a priori estimates for solutions of fully nonlinear equations
• 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 Brunn-Minkowski inequality and a Minkowski problem for \(\mathcal{A} \)-harmonic Green's function
• 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
• Prescribing harmonic measure on convex domains
• A Minkowski problem for electrostatic capacity
• The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation
• The discrete planar \(L_0\)-Minkowski problem
• Exploiting log-capacity in convex geometry
• The \(L_{p}\)-Minkowski problem for \(-n < p < 1\)
• On the \(L_p\) dual Minkowski problem
• On the planar dual Minkowski problem
• The \(L_p\)-Aleksandrov problem for \(L_p\)-integral curvature
• The \(p\)-capacitary Orlicz-Hadamard variational formula and Orlicz-Minkowski problems
• The \(L_{p}\) dual Minkowski problem for \(p\) 1 and \(q\) 0
• \(L_{p}\) dual curvature measures
• \(L^p\) Christoffel-Minkowski problem: the case \(1< p<k+1\)
• Convex hypersurfaces of prescribed curvatures
• On the Christoffel-Minkowski problem of Firey's \(p\)-sum
• On the regularity of solutions to a generalization of the Minkowski problem
• On the case of equality in the Brunn-Minkowski inequality for capacity
• The \(L_p\) Minkowski problem for the electrostatic \(\mathfrak{p}\)-capacity
• The logarithmic Minkowski problem for polytopes
• Note on an eigenvalue problem with applications to a Minkowski type regularity problem in \(\mathbb{R}^n\)
• Smoothness in the \(L_p\) Minkowski problem for \(p<1\)
• The \(L_p\) Minkowski problem for torsion
• The \(L _p\) capacitary Minkowski problem for polytopes
• The Orlicz version of the \(L_p\) Minkowski problem for \(- n < p < 0\)
• Nonuniqueness of solutions to the \(L_p\)-Minkowski problem
• On the uniqueness of \(L_p\)-Minkowski problems: the constant \(p\)-curvature case in \(\mathbb{R}^3\)
• Smooth solutions to the \(L_p\) dual Minkowski problem
• On the \(L_{p}\) Minkowski problem for polytopes
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• The direct method in the calculus of variations for convex bodies
• Regularity and free boundary regularity for the $p$-Laplace operator in Reifenberg flat and Ahlfors regular domains
• The Minkowski problem for the torsional rigidity
• Some regularity properties of solutions of Monge Ampère equation
• On the regularity of the solution of then-dimensional Minkowski problem
• The logarithmic Minkowski problem for non-symmetric measures
• The logarithmic Minkowski problem
• The Brunn-Minkowski Inequality and A Minkowski Problem for Nonlinear Capacity
• Convex Bodies The Brunn-MinkowskiTheory
• $p$-Means of Convex Bodies.
• The Weyl and Minkowski problems in differential geometry in the large
• The Monge-Ampère equation
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