On the uniqueness of \(L_p\)-Minkowski problems: the constant \(p\)-curvature case in \(\mathbb{R}^3\)

DOI10.1016/j.aim.2015.02.021zbMath1329.52003arXiv1503.02358OpenAlexW1860579665MaRDI QIDQ2354384

Lu Xu, Jiakun Liu, Yong Huang

Publication date: 13 July 2015

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

Full work available at URL: https://arxiv.org/abs/1503.02358

zbMATH Keywords

uniquenessconvex bodyMonge-Ampère equation\(L_p\)-Minkowski problem

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Monge-Ampère equations (35J96)

Related Items (52)

On the 2-dimensional dual Minkowski problem ⋮ On a non-homogeneous version of a problem of Firey ⋮ A generalization of \(L_{p}\)-Brunn-Minkowski inequalities and \(L_{p}\)-Minkowski problems for measures ⋮ Hadamard variational formulas for \(p\)-torsion and \(p\)-eigenvalue with applications ⋮ Mirror symmetric solutions to the centro-affine Minkowski problem ⋮ Multiple solutions of the planar \(L_p\) dual Minkowski problem ⋮ On the \(L_p\) dual Minkowski problem ⋮ On the planar dual Minkowski problem ⋮ Multiple solutions of the \(L_{p}\)-Minkowski problem ⋮ On the uniqueness and continuity of the dual area measure ⋮ On a planar conformal curvature problem ⋮ The \(L_p\)-Brunn-Minkowski inequality for \(p<1\) ⋮ Local 𝐿^{𝑝}-Brunn–Minkowski inequalities for 𝑝<1 ⋮ Deforming a convex hypersurface by anisotropic curvature flows ⋮ Smooth solutions to the \(L_p\) dual Minkowski problem ⋮ Uniqueness of self‐similar solutions to flows by quotient curvatures ⋮ A flow method to the Orlicz-Aleksandrov problem ⋮ A flow approach to the planar Lp$L_p$ Minkowski problem ⋮ Uniqueness of solutions to a class of mixed Hessian quotient type equations ⋮ Variational analysis of the planar \(L_p\) dual Minkowski problem ⋮ On the general dual Orlicz-Minkowski problem ⋮ Continuity of the solution to the \(L_p\) Minkowski problem in Gaussian probability space ⋮ A generalized rotationally symmetric case of the centroaffine Minkowski problem ⋮ Existence of solutions to the Orlicz-Minkowski problem ⋮ A remark on rotationally symmetric solutions to the centroaffine Minkowski problem ⋮ A \(L_p\) Brunn-Minkowski theory for logarithmic capacity ⋮ A flow method for the dual Orlicz–Minkowski problem ⋮ Continuity of the solution to the even Lp Minkowski problem for 0 < p < 1 in the plane ⋮ Nonexistence of maximizers for the functional of the centroaffine Minkowski problem ⋮ Noncompact L_p-Minkowski problems ⋮ Continuity of the solution to the dual Minkowski problem for negative indices ⋮ The logarithmic Minkowski problem for non-symmetric measures ⋮ Dual Orlicz mixed affine quermassintegrals ⋮ Flow expanding by Gauss curvature to $L_p$ dual Minkowski problems ⋮ On the \(L_{p}\) Monge-Ampère equation ⋮ On the planar \(L_p\)-Minkowski problem ⋮ Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems ⋮ Unnamed Item ⋮ Existence and uniqueness of solutions to Orlicz Minkowski problems involving \(0 < p < 1\) ⋮ Stable solution of the Logarithmic Minkowski problem in the case of hyperplane symmetries ⋮ The Orlicz Minkowski problem involving \(0 < p < 1 \): from one constant to an infinite interval ⋮ The \(L_p\) Minkowski problem for torsion ⋮ The \(L_p\)-Gaussian Minkowski problem ⋮ The 𝐿_{𝑝} Aleksandrov problem for origin-symmetric polytopes ⋮ Continuity of the solution to the $L_{p}$ Minkowski problem ⋮ Variational characterization for the planar dual Minkowski problem ⋮ Continuity of the solution to the even logarithmic Minkowski problem in the plane ⋮ An extension of Minkowski's theorem and its applications to questions about projections for measures ⋮ The dual Minkowski problem for symmetric convex bodies ⋮ The L_p Minkowski problem for q-capacity ⋮ The planar Orlicz Minkowski problem for \(p=0\) without even assumptions ⋮ Geometry of log-concave functions: the \(L_p\) Asplund sum and the \(L_p\) Minkowski problem

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