Anisotropic Gauss curvature flows and their associated Dual Orlicz-Minkowski problems

DOI10.1017/prm.2020.102zbMath1485.35252OpenAlexW3210792873WikidataQ114117848 ScholiaQ114117848MaRDI QIDQ5861965

Li Chen, Di Wu, Qiang Tu, Ni Xiang

Publication date: 3 March 2022

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.2020.102

zbMATH Keywords

Gauss curvature flowconvex hypersurfaceMonge-Ampère type equation

Mathematics Subject Classification ID

Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Monge-Ampère equations (35J96)

Related Items (2)

Smooth solutions to the Gauss image problem ⋮ The \(L_p\) Gauss image problem

Cites Work

• The dual Minkowski problem for negative indices
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• Deforming convex hypersurfaces by the \(n\)th root of the Gaussian curvature
• An expansion of convex hypersurfaces
• Evolving convex curves
• Motion of hypersurfaces by Gauss curvature
• A logarithmic Gauss curvature flow and the Minkowski problem.
• A unified flow approach to smooth, even \(L_p\)-Minkowski problems
• Entropy and a convergence theorem for Gauss curvature flow in high dimension
• Asymptotic behavior of flows by powers of the Gaussian curvature
• Gauss curvature flow: The fate of the rolling stones
• Contraction of convex hypersurfaces by their affine normal
• Surfaces moving by powers of Gauss curvature
• The \(L_p\) dual Minkowski problem and related parabolic flows
• Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems
• The dual Orlicz-Brunn-Minkowski theory
• Smooth solutions to the \(L_p\) dual Minkowski problem
• Flow by powers of the Gauss curvature
• A flow method for the dual Orlicz–Minkowski problem
• Deforming a hypersurface by its Gauss-Kronecker curvature
• Existence of convex hypersurfaces with prescribed Gauss-Kronecker curvature
• Shapes of worn stones
• Classification of limiting shapes for isotropic curve flows
• The logarithmic Minkowski problem

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