A new renormalized volume-type invariant

WU JINYANGWe define a new conformal invariant on complete noncompact hyperbolic surfaces that can be conformally compactified to bounded domains in .We study and compute this invariant up to doubly connected surfaces.Our results give a new geometric criterion for choosing canonical representations of bounded domains in . 1. Introduction 43 2. A technical tool 46 3. Doubly connected domains 48 4. Rigidity of doubly connected domains 51 Appendix 53