分野別セミナー

The steady state space is a model for the universe proposed by Bondi, Gold and Hoyle which is homogeneous and isotropic. A mathematical model of this space corresponds with the Lorentzian analogue to the upper half-space model of hyperbolic space. In this talk we consider spacelike surfaces with constant mean curvature (cmc) and we discuss some problems on the shape of a compact cmc surface or the Dirichlet problem associated to the cmc equation. We show some of the techniques employed in this context such as the maximum principle, the Alexandrov reflection method or methods for obtaining a priori estimates of cmc graphs.