Generalized isometric spheres and fundamental domains for discrete subgroups of $PU(1,n; \mathbf {C})$
Kamiya, Shigeyasu
Proc. Japan Acad. Ser. A Math. Sci., Tome 79 (2003) no. 3, p. 105-109 / Harvested from Project Euclid
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Let $G$ be a discrete subgroup of $PU(1,n; \mathbf{C})$. For a boundary point $y$ of the Siegel domain, we define the generalized isometric sphere $I_y(f)$ of an element $f$ of $PU(1,n; \mathbf{C})$. By using the generalized isometric spheres of elements of $G$, we construct a fundamental domain $P_y(G)$ for $G$, which is regarded as a generalization of the Ford domain. And we show that the Dirichlet polyhedron $D(w)$ for $G$ with center $w$ convereges to $P_y(G)$ as $w \rightarrow y$. Some results are also found in [5], but our method is elementary.
Publié le : 2003-05-14
Classification:  Generalized isometric sphere,  discrete subgroup,  $PU(1,n;\mathbf {C})$,  30F40,  22E40 
@article{1116443679,
     author = {Kamiya, Shigeyasu},
     title = {Generalized isometric spheres and fundamental domains for discrete subgroups of $PU(1,n; \mathbf {C})$},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {79},
     number = {3},
     year = {2003},
     pages = { 105-109},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1116443679}
}

Kamiya, Shigeyasu. Generalized isometric spheres and fundamental domains for discrete subgroups of $PU(1,n; \mathbf {C})$. Proc. Japan Acad. Ser. A Math. Sci., Tome 79 (2003) no. 3, pp.  105-109. http://gdmltest.u-ga.fr/item/1116443679/