Ledoux-type rigidity results on manifolds with boundary in the presence of symmetries. (September 2020)

• Record Type: Journal Article
• Authors: Cotsiolis, Athanase; Labropoulos, Nikos
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 53C24 -- 58D19 -- 41A44 -- 35B33; Rigidity -- Supercritical Hardy–Sobolev inequalities -- Solid torus -- Manifolds with boundary; 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.2020.111887
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a 3 -dimensional complete Riemannian manifold ( M, g ) with boundary and assuming that an optimal Sobolev or Hardy–Sobolev inequality holds with the same best constant as in the case of the solid torus T we investigate the relationship between the geometry of such a manifold and that of the solid torus and we prove Ledoux-type rigidity results (see in Ledoux (1999)) giving a positive answer to a question posed to us by the referee of our recently published paper Cotsiolis and Labropoulos (2018). Some generalization results, for n -dimensional Riemannian manifolds ( M, g ) with n > 3, are also presented.