Orateur(s)  Tatiana ZOLOTAREVA  CMLS, Ecole Polytechnique,

Titre  Nonconvex constant mean curvature surfaces in generic Riemannian 3manifolds 
Date  25/01/2016 
Horaire  14:00 à 16:00 

Diffusion  
Résume  In Euclidean 3space, 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 3manifolds 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 nonzero eigenvalue of the Hessian of the scalar curvature. 
Salle  salle 2015 
Adresse  Sophie Germain 