The volume-preserving Willmore flow. (May 2023)

• Record Type: Journal Article
• Authors: Rupp, Fabian
• Is Part Of: Nonlinear analysis. Volume 230(2023)
• Publication Date: 2023-05
• Subjects: primary 53E40 35B40 -- secondary 35K41; Willmore flow -- Fixed volume -- Blow-up -- Łojasiewicz–Simon inequality -- Nonlocal geometric evolution equation; 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.2023.113220
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a closed surface in R 3 evolving by the volume-preserving Willmore flow and prove a lower bound for the existence time of smooth solutions. For spherical initial surfaces with Willmore energy below 8 π we show long time existence and convergence to a round sphere by performing a suitable blow-up and by proving a constrained Łojasiewicz–Simon inequality.