On complete gradient Schouten solitons. (August 2022)

• Record Type: Journal Article
• Authors: Borges, Valter
• Is Part Of: Nonlinear analysis. Volume 221(2022)
• Publication Date: 2022-08
• Subjects: primary 35Q51 53B20 53C20 53C25 -- secondary 34A40; Schouten soliton -- Schouten flow -- Gradient estimate -- Volume estimate; 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.2022.112883
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we prove an optimal inequality between the potential function of a complete Schouten soliton and the norm of its gradient. We also prove that these metrics have bounded scalar curvature of defined sign. As an application, we prove that the potential function of a Shrinking Schouten soliton grows linearly and provide optimal estimates for the growth of the volume of geodesic balls.