Lower bounds for the length of the second fundamental form via the first eigenvalue of the p-Laplacian. (July 2023)

• Record Type: Journal Article
• Authors: dos Santos, Fábio R.; Soares, Matheus N.
• Is Part Of: Nonlinear analysis. Volume 232(2023)
• Publication Date: 2023-07
• Subjects: primary 53C42 -- secondary 53A10 53C23; Closed and compact submanifolds -- Minimal submanifolds -- Bochner formula -- First eigenvalue -- p-Laplacian; 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.2023.113251
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: A suitable Bochner type formula for a certain divergence type operator is obtained. As an application, several integral inequalities involving the squared norm of the second fundamental form of a minimal compact (with or without boundary) submanifold in the sphere and the first eigenvalue of p -Laplacian are established. Finally, lower bounds of the second fundamental form of a such minimal submanifold are proven.