Ledoux-type rigidity results on manifolds with boundary in the presence of symmetries. (September 2020) - Cotsiolis, Athanase; Labropoulos, Nikos
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.