Ancient finite entropy flows by powers of curvature in R2. (March 2022)

• Record Type: Journal Article
• Authors: Choi, Kyeongsu; Sun, Liming
• Is Part Of: Nonlinear analysis. Volume 216(2022)
• Publication Date: 2022-03
• Subjects: primary 53C44 53A04 -- secondary 35K55; Curve shortening flow -- Ancient solutions -- Fully nonlinear parabolic PDEs; 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.2021.112673
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We show the existence of non-homothetic ancient flows by powers of curvature embedded in R 2 whose entropy is finite. We determine the Morse indices and kernels of the linearized operator of shrinkers to the flows, and construct ancient flows by using unstable eigenfunctions of the linearized operator.