Abstract
The following are notes on the geometry of the bidisk, H 2 × H 2. In particular, we examine the properties of equidistant surfaces in the bidisk.
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Bridson, M.R., Haefliger, A.: Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 319, Springer, Berlin (1999)
Busemann H.: The Geometry of Geodesics, Pure and Applied Mathematics. Academic Press, London (1955)
Drumm T.A., Poritz J.A.: Ford and Dirichlet domains for cyclic subgroups of PSL 2(C) acting on \({H^3_R}\) and \({\partial H^3_R}\). Conform. Geom. Dyn. 3, 116–150 (1999)
Ehrlich P.E., Im Hof H.-C.: Dirichlet regions in manifolds without conjugate points. Comment. Math. Helv. 54(4), 642–658 (1979)
Eskin, A., Farb, B.: Quasi-flats in H2 × H2, Lie groups and ergodic theory, Tata Inst. Fund. Res. Stud. Math., vol. 14, Tata Inst. Fund. Res., pp. 75–103 (1998)
Goldman W.M.: Complex Hyperbolic Geometry, Oxford Mathematical Monographs. Oxford University Press, Oxford (1999)
Helgason, S.: Differential Geometry, Lie Groups, and Symmetric Spaces, Graduate Studies in Mathematics, vol. 34, American Mathematical Society, Providence (2001)
Jørgensen T.: On cyclic groups of Moebius transformations. Math. Scand. 33, 250–260 (1973)
Phillips M.B.: Dirichlet polyhedra for cyclic groups in complex hyperboolic space. Proc. Am. Math. Soc. 115(1), 221–228 (1992)
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Charette, V., Drumm, T.A. & Lareau-Dussault, R. Equidistant hypersurfaces of the bidisk. Geom Dedicata 163, 275–284 (2013). https://doi.org/10.1007/s10711-012-9748-7
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DOI: https://doi.org/10.1007/s10711-012-9748-7