Continuity of the solution to the even Lp Minkowski problem for 0 < p < 1 in the plane

DOI10.1142/S0129167X20501013zbMath1460.52012OpenAlexW3082228090MaRDI QIDQ5146644

Publication date: 26 January 2021

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129167x20501013

zbMATH Keywords

convex body $L_p$ Minkowski problem $L_p$ surface area measure $L_p$ Minkowski inequality

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (2) dimensions (including convex curves) (52A10)

Related Items (3)

A flow approach to the planar Lp$L_p$ Minkowski problem ⋮ Lp$L_p$‐cosine transform of the (p,q)${(p,q)}$‐th dual curvature measure ⋮ Continuity of the solution to the $L_p$ Minkowski problem in Gaussian probability space

Cites Work

Unnamed Item
Unnamed Item
Mirror symmetric solutions to the centro-affine Minkowski problem
The affine Sobolev-Zhang inequality on BV($\mathbb R^n)$
On the Orlicz Minkowski problem for polytopes
The log-Brunn-Minkowski inequality
The dual Minkowski problem for negative indices
Sharp convex Lorentz-Sobolev inequalities
An asymmetric affine Pólya-Szegő principle
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
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
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 discrete planar $L_0$-Minkowski problem
The affine Sobolev inequality.
Existence of solutions to the even dual Minkowski problem
On the $L_p$ 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.
Gauss curvature flow: The fate of the rolling stones
On the regularity of solutions to a generalization of the Minkowski problem
Rotationally symmetric solutions to the $L_p$-Minkowski problem
On the $L_{p}$ Monge-Ampère equation
The logarithmic Minkowski problem for polytopes
Continuity of the solution to the even logarithmic Minkowski problem in the plane
The $L_p$ Minkowski problem for polytopes for $0 < p < 1$
On the uniqueness of $L_p$-Minkowski problems: the constant $p$-curvature case in $\mathbb{R}^3$
$L_p$ Minkowski problem with not necessarily positive data
Asymmetric affine $L_p$ Sobolev inequalities
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
Continuity of the solution to the $L_{p}$ Minkowski problem
On the regularity of the solution of then-dimensional Minkowski problem
Continuity of the solution to the dual Minkowski problem for negative indices
On the $L_{p}$-Minkowski problem
The logarithmic Minkowski problem
The Lp Minkowski problem for polytopes for p<0
Convex Bodies The Brunn-MinkowskiTheory
On Differential Geometry in the Large, I (Minkowski's Problem)
The Weyl and Minkowski problems in differential geometry in the large

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