7 nov 2017 -- 14:30
Aula Dal Passo, Dip.Matematica, Università "Tor Vergata", Roma
Abstract.
According to a famous result by A.D. Alexandrov, the only embedded, oriented, compact, constant mean curvature (CMC) surfaces in the Euclidean 3-space are round spheres. In particular there is no CMC embedded torus. We investigate the problem of embedded tori for a class of radially symmetric, prescribed mean curvature functions converging to a constant at infinity. Under suitable conditions, we construct a sequence of embedded tori. Such surfaces are close to sections of unduloids with small necksize, folded along circumferences centered at the origin and with larger and larger radii. The construction involves a deep study of the corresponding Jacobi operators, an application of the Lyapunov-Schmidt reduction method and some variational argument. This is a joint work with Monica Musso (Pontificia Universidad Catolica de Chile).