Volume of C1,α-boundary domain in extended hyperbolic space

Yunhi Cho, Hyuk Kim

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We consider the projectivization of Minkowski space with the analytic continuation of the hyperbolic metric and call this an extended hyperbolic space. We can measure the volume of a domain lying across the boundary of the hyperbolic space using an analytic continuation argument. In this paper we show this method can be further generalized to find the volume of a domain with smooth boundary with suitable regularity in dimension 2 and 3. We also discuss that this volume is invariant under the group of hyperbolic isometries and that this regularity condition is sharp.

Original languageEnglish
Pages (from-to)1143-1158
Number of pages16
JournalJournal of the Korean Mathematical Society
Issue number6
StatePublished - Nov 2006


  • Analytic continuation
  • Hyperbolic space
  • Volume


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