Volume of $C^{1,\alpha}$-boundary domain in extended hyperbolic space
Metric Geometry
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0612374,
title = {Volume of $C^{1,\alpha}$-boundary domain in extended hyperbolic space},
author = {Yunhi Cho and Hyuk Kim},
journal= {arXiv preprint arXiv:math/0612374},
year = {2007}
}