A flow method to the Orlicz-Aleksandrov problem

DOI10.1016/j.jfa.2022.109825OpenAlexW4312193536MaRDI QIDQ2680206

Jiaqian Liu, Di Ma, Jinrong Hu

Publication date: 30 January 2023

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.06702

zbMATH Keywords

Monge-Ampère equationgeometric flowOrlicz Aleksandrov problem

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators (35K86)

Related Items (1)

On the existence of solutions to the Orlicz Aleksandrov problem

Cites Work

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• Prescription of Gauss curvature using optimal mass transport
• On the Orlicz Minkowski problem for polytopes
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Orlicz centroid bodies
• The even Orlicz Minkowski problem
• Orlicz projection bodies
• An expansion of convex hypersurfaces
• A logarithmic Gauss curvature flow and the Minkowski problem.
• The \(L_{p}\)-Minkowski problem for \(-n < p < 1\)
• General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. I
• 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 and related parabolic flows
• Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems
• Asymptotic convergence for a class of fully nonlinear curvature flows
• 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 \(\mathbb{R}^3\)
• The planar \(L_{p}\)-Minkowski problem for \(0<p<1\)
• Embedding \(\mathbb S^n\) into \(\mathbb R^{n+1}\) with given integral Gauss curvature and optimal mass transport on \(\mathbb S^n\)
• Smooth solutions to the \(L_p\) dual Minkowski problem
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• Flow by powers of the Gauss curvature
• A flow method for the dual Orlicz–Minkowski problem
• The Existence of Convex Body with Prescribed Curvature Measures
• Shapes of worn stones
• On the discrete Orlicz Minkowski problem
• On the $L_{p}$-Minkowski problem
• The Orlicz Aleksandrov Problem for Orlicz Integral Curvature
• The 𝐿_{𝑝} Aleksandrov problem for origin-symmetric polytopes
• Convex Bodies The Brunn-MinkowskiTheory
• Some Means of Convex Bodies

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