Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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VOLUME OF C1,α-BOUNDARY DOMAIN IN EXTENDED HYPERBOLIC SPACE

  • Cho, Yun-Hi (Department of Mathematics University of Seoul) ;
  • Kim, Hyuk (Department of Mathematics Seoul National University)
  • Published : 2006.11.01
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Abstract

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.

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References

  1. Y. Cho and H. Kim, The analytic continuation of hyperbolic space, (preprint)

Cited by

  1. GEOMETRIC AND ANALYTIC INTERPRETATION OF ORTHOSCHEME AND LAMBERT CUBE IN EXTENDED HYPERBOLIC SPACE vol.50, pp.6, 2013, https://doi.org/10.4134/JKMS.2013.50.6.1223
  2. The analytic continuation of hyperbolic space vol.161, pp.1, 2012, https://doi.org/10.1007/s10711-012-9698-0