Hyperbolic energy and Maskit gluings

Abstract

We derive a formula for the energy of asymptotically locally hyperbolic (ALH) manifolds obtained by a gluing at infinity of two ALH manifolds. As an application we show that there exist three-dimensional conformally compact ALH manifolds either without boundary or with toroidal black hole boundary, with connected conformal infinity of higher genus, with constant negative scalar curvature, and with negative mass.

48 pages, 7 figures, v2: various improvements of the presentation, accepted for Advances in Theoretical and Mathematical Physics