Colding Minicozzi entropy in hyperbolic space. (September 2021)

• Record Type: Journal Article
• Authors: Bernstein, Jacob
• Is Part Of: Nonlinear analysis. Volume 210(2021)
• Publication Date: 2021-09
• Subjects: 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.2021.112401
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This note introduces a notion of entropy for submanifolds of hyperbolic space analogous to the one introduced by Colding and Minicozzi for submanifolds of Euclidean space. Several properties are proved for this quantity including monotonicity along mean curvature flow in low dimensions and a connection with the conformal volume.