Carron, Gilles Faber-Krahn isoperimetric inequalities and consequences. (Inégalités isopérimétriques de Faber-Krahn et conséquences.) (French) Zbl 0884.58088 Besse, Arthur L. (ed.), Actes de la table ronde de géométrie différentielle en l’honneur de Marcel Berger, Luminy, France, 12–18 juillet, 1992. Paris: Société Mathématique de France. Sémin. Congr. 1, 205-232 (1996). The author shows that a complete non-compact Riemannian manifold satisfies a Faber-Krahn inequality if and only if it satisfies a Sobolev one. He also gives some other equivalent properties such as bound on heat kernel or bound on Green functions. He also proves that we have a uniform lower bound for the volume of geodesic balls in terms of the Faber-Krahn inequality.For the entire collection see [Zbl 0859.00016]. Reviewer: M.Puta (Timişoara) Cited in 1 ReviewCited in 34 Documents MSC: 58J35 Heat and other parabolic equation methods for PDEs on manifolds 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 58C40 Spectral theory; eigenvalue problems on manifolds Keywords:isoperimetric inequalities; Sobolev inequality; Faber-Krahn inequality PDF BibTeX XML Cite \textit{G. Carron}, Sémin. Congr. 1, 205--232 (1996; Zbl 0884.58088) OpenURL