# Séminaires : Séminaire de Géométrie

 Equipe(s) : gd, Responsables : L. Hauswirth, P. Laurain, R. Souam, E. Toubiana Email des responsables : Salle : https://bbb-front.math.univ-paris-diderot.fr/recherche/pau-6ha-of4-mea Adresse : Sophie Germain Description Archive avant 2014 Hébergé par le projet Géométrie et Dynamique de l’IMJ-PRG

 Orateur(s) Tatiana ZOLOTAREVA - CMLS, Ecole Polytechnique, Titre Nonconvex constant mean curvature surfaces in generic Riemannian 3-manifolds Date 25/01/2016 Horaire 14:00 à 16:00 Diffusion Résume In Euclidean 3-space, Hopf's Theorem asserts that round spheres are the only topological spheres whose mean curvature is constant. In 1990, R. Ye proved the existence of embedded constant mean curvature hypersurfaces in Riemannian manifolds obtained by perturbing geodesic spheres centered near nondegenerate critical points of the scalar curvature function. In our result we prove the existence in ''generic Riemannian 3-manifolds of topological spheres that have large constant mean curvature but are not convex. These surfaces are obtained by perturbing the connected sums of two tangent geodesic spheres of small radii whose centers are lined up along a geodesic which passes through a critical point of the scalar curvature function with velocity equal to a unit eigenvector associated to a simple non-zero eigenvalue of the Hessian of the scalar curvature. Salle https://bbb-front.math.univ-paris-diderot.fr/recherche/pau-6ha-of4-mea Adresse Sophie Germain