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VOLUME OF C1,α-BOUNDARY DOMAIN IN EXTENDED HYPERBOLIC SPACE
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 Title & Authors
VOLUME OF C1,α-BOUNDARY DOMAIN IN EXTENDED HYPERBOLIC SPACE
Cho, Yun-Hi; Kim, Hyuk;
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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.ᰉ匀̀歭猏ë貀鳬袘駭验
 Keywords
hyperbolic space;volume;analytic continuation;
 Language
English
 Cited by
1.
RIGONOMETRY IN EXTENDED HYPERBOLIC SPACE AND EXTENDED DE SITTER SPACE,;

대한수학회보, 2009. vol.46. 6, pp.1099-1133 crossref(new window)
2.
GEOMETRIC AND ANALYTIC INTERPRETATION OF ORTHOSCHEME AND LAMBERT CUBE IN EXTENDED HYPERBOLIC SPACE,;;

대한수학회지, 2013. vol.50. 6, pp.1223-1256 crossref(new window)
1.
The analytic continuation of hyperbolic space, Geometriae Dedicata, 2012, 161, 1, 129  crossref(new windwow)
2.
GEOMETRIC AND ANALYTIC INTERPRETATION OF ORTHOSCHEME AND LAMBERT CUBE IN EXTENDED HYPERBOLIC SPACE, Journal of the Korean Mathematical Society, 2013, 50, 6, 1223  crossref(new windwow)
 References
1.
Y. Cho and H. Kim, The analytic continuation of hyperbolic space, (preprint)