Séminaires : Séminaire de Géométrie

Equipe(s) : gd,
Responsables :L. Hauswirth, P. Laurain, R. Souam, E. Toubiana
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Salle : 1013
Adresse :Sophie Germain
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Orateur(s) Tatiana ZOLOTAREVA - CMLS, Ecole Polytechnique,
Titre Nonconvex constant mean curvature surfaces in generic Riemannian 3-manifolds
Date25/01/2016
Horaire14:00 à 16:00
Diffusion
RésumeIn 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.
Salle1013
AdresseSophie Germain
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