2020/10/02 by Hongjie Ju, Boya Li, BoYa Li +2 · 7 citations
Mathematics · #Applied mathematics #Convex function #Convex optimization #Curvature #Euclidean space #Flow (mathematics) #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Hessian matrix #Hypersurface #Mathematical analysis #Mathematics #Mean curvature #Mean curvature flow #Minkowski space #Point processes and geometric inequalities #Principal curvature #Pure mathematics #Regular polygon #Subderivative #Support function #math.AP #math.DG #msc:35J75 #msc:35J96 #msc:53A07 #msc:53A15
paper · pdf · open access · doi:10.1515/ans-2020-2108
published in Advanced Nonlinear Studies 21(1), 155-166 (De Gruyter) · 19 pages. arXiv admin note: text overlap with arXiv:2005.02376
openalex publication_date 2020/10/02 · arxiv created 2020/11/20 · arxiv updated 2020/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract In this paper, we consider a fully nonlinear curvature flow of a convex hypersurface in the Euclidean 𝑛-space. This flow involves 𝑘-th elementary symmetric function for principal curvature radii and a function of support function. Under some appropriate assumptions, we prove the long-time existence and convergence of this flow. As an application, we give the existence of smooth solutions to the Orlicz–Christoffel–Minkowski problem.