A unified flow approach to smooth, even Lp-Minkowski problems

2016/08/31 by Paul Bryan, Mohammad N. Ivaki, Julian Scheuer · 42 citations
Mathematics · #Calculus (dental) #Class (philosophy) #Curvature #Flow (mathematics) #Geometric Analysis and Curvature Flows #Mean curvature flow #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #math.AP #math.DG

paper · pdf · doi:10.2140/apde.2019.12.259

published in Analysis & PDE 12(2), 259-280 (Mathematical Sciences Publishers) · 21 pages. Comments are welcome

openalex created_date 2016/08/23 · arxiv created 2018/05/06 · openalex publication_date 2018/10/07 · arxiv updated 2018/10/10 · openalex updated_date 2026/08/06

Abstract

We study long-time existence and asymptotic behavior for a class of anisotropic, expanding curvature flows. For this we adapt new curvature estimates, which were developed by Guan, Ren and Wang to treat some stationary prescribed curvature problems. As an application we give a unified flow approach to the existence of smooth, even [math] -Minkowski problems in [math] for [math] .

Citations

• On the regularity of the solution of the n ‐dimensional Minkowski problem
• On the Existence of a Closed Convex Surface Realizing a Given Riemannian Metric
• The dirichlet problem for nonlinear second‐order elliptic equations I. Monge‐ampégre equation
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens.
• Global C2‐Estimates for Convex Solutions of Curvature Equations

Cited by

• Deforming a Convex Hypersurface by Anisotropic Curvature Flows