Seminari del Dipartimento
Geometria Compact embedded surfaces with constant mean curvature in
S^2 imes R Jose Miguel Manzano 04-07-2019 - 14:30 Largo San Leonardo Murialdo,1 - Pal.C - Aula 211
Compact embedded surfaces with constant mean curvature H>0 in S^2 imes R are symmetric bigraphs over domains of the 2-sphere S^2 as an application of Alexandrov reflection principle. Therefore, such surfaces coincide with solutions to the overdetermined elliptic problem associated with the constant mean curvature equation, with a capillarity condition and zero values along the boundary. In this talk, we will give a sharp bound for the curvature of the boundaries of the aforesaid domains (as spherical curves), and then apply it to obtain examples of compact embedded surfaces with arbitrary genus and constant mean curvature 0<H<1/2. This construction will involve the use of a conjugate technique and the solution of the Plateau problem in certain Berger spheres. This talk is based on a joint work with F. Torralbo (University of Granada). |