Minimal hypersurfaces with low index in the real projective space. (May 2022)

• Record Type: Journal Article
• Authors: Batista, Márcio; Martins, Matheus B.
• Is Part Of: Nonlinear analysis. Volume 218(2022)
• Publication Date: 2022-05
• Subjects: 53A10 -- 53C42 -- 58J20; Minimal hypersurfaces -- Morse index -- Min–max -- Gap; 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.2021.112776
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we use suitable ideas from the min–max theory in finite dimension to prove that the only compact two-sided minimal and constant scalar curvature hypersurfaces in the real projective space with Morse index less or equal to two are the totally geodesic sphere or the Clifford minimal hypersurfaces.