Recent Progress in Double Beta Decay

At least one neutrino has a mass of about 50 meV or larger. However, the absolute mass scale for the neutrino remains unknown. Studies of double beta decay offer hope for determining the absolute mass scale. Furthermore, the critical question: Is the neutrino its own antiparticle? is unanswered. In particular, zero-neutrino double beta decay can address the issues of lepton number conservation, the particle-antiparticle nature of the neutrino, and its mass. A summary of the recent progress in double beta decay, and the related technologies will be discussed in the context of the future double beta decay program.Comment: Invited submission to Mod. Phys. Lett.

The Green's function and the Ahlfors map

The classical Green's function associated to a simply connected domain in the complex plane is easily expressed in terms of a Riemann mapping function. The purpose of this paper is to express the Green's function of a finitely connected domain in the plane in terms of a single Ahlfors mapping of the domain, which is a proper holomorphic mapping of the domain onto the unit disc that is the analogue of the Riemann map in the multiply connected setting.Comment: 14 page