Combinatorial p-th Ricci flows on surfaces. (October 2021)

• Record Type: Journal Article
• Authors: Lin, Aijin; Zhang, Xiaoxiao
• Is Part Of: Nonlinear analysis. Volume 211(2021)
• Publication Date: 2021-10
• Subjects: 52C26 -- 53C44; Circle packings -- Combinatorial Ricci/Calabi flow -- Combinatorial Ricci potential; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112417
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: For any p > 1 and triangulated surfaces, we introduce the combinatorial p -th Ricci flow which exactly equals the combinatorial Ricci flow first introduced by Chow-Luo (Chow and Luo, 2003) when p = 2 . Then we show the long time existence and convergence of the solution to the combinatorial p -th Ricci flow. Our results partially generalize Chow-Luo's work on the combinatorial Ricci flow from p = 2 to any p > 1 .