J. Korean Math. Soc. 2006; 43(6): 1143-1158
Printed November 1, 2006
Copyright © The Korean Mathematical Society.
Yunhi Cho and Hyuk Kim
University of Seoul, University of Seoul
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.
Keywords: hyperbolic space, volume, analytic continuation
MSC numbers: 51M10, 51M25, 53C50
2013; 50(6): 1223-1256
2016; 53(4): 737-767
2013; 50(6): 1311-1332
1996; 33(1): 137-144
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd