A class of Gauss curvature flows and its applications to an even dual Orlicz-Minkowski type problem

DOI10.1016/j.na.2022.112798zbMath1485.35255OpenAlexW4210269343WikidataQ114146016 ScholiaQ114146016MaRDI QIDQ2078598

Di Wu, Qiang Tu, Si-yuan Xie

Publication date: 1 March 2022

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2022.112798

zbMATH Keywords

existenceMonge-Ampère-type equationanisotropic Gauss curvature flow

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Monge-Ampère equations (35J96)

Cites Work

• Deforming a hypersurface by Gauss curvature and support function
• The dual Minkowski problem for negative indices
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Deforming convex hypersurfaces by the \(n\)th root of the Gaussian curvature
• An expansion of convex hypersurfaces
• Evolving plane curves by curvature in relative geometries. II
• The inverse mean curvature flow and the Riemannian Penrose inequality
• A logarithmic Gauss curvature flow and the Minkowski problem.
• The discrete planar \(L_0\)-Minkowski problem
• A unified flow approach to smooth, even \(L_p\)-Minkowski problems
• Existence of solutions to the even dual Minkowski problem
• General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. I
• On the \(L_p\) dual Minkowski problem
• The \(L_p\)-Aleksandrov problem for \(L_p\)-integral curvature
• Necessary subspace concentration conditions for the even dual Minkowski problem
• Asymptotic behavior of flows by powers of the Gaussian curvature
• The \(L_{p}\) dual Minkowski problem for \(p\) 1 and \(q\) 0
• Remarks on the entropy and Harnack estimates for the Gauss curvature flow
• Variations of a class of Monge-Ampère-type functionals and their applications
• The \(L_p\) dual Minkowski problem and related parabolic flows
• Existence of smooth even solutions to the dual Orlicz-Minkowski problem
• The logarithmic Minkowski problem for polytopes
• General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. II
• Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems
• Variational characterization for the planar dual Minkowski problem
• 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
• Flow by powers of the Gauss curvature
• Non-scale-invariant inverse curvature flows in Euclidean space
• A flow method for the dual Orlicz–Minkowski problem
• Deforming a hypersurface by its Gauss-Kronecker curvature
• Shapes of worn stones
• The logarithmic Minkowski problem for non-symmetric measures
• On the $L_{p}$-Minkowski problem
• The logarithmic Minkowski problem