arXiv subjects

Uddhab Roy

Publications and source records attributed to Uddhab Roy.

2 recordsLinked to original sources

arXiv2023

Construction of Fuchsian Schottky group with conformal boundary at infinity

In this article, we have constructed an interesting type of generalized Schottky group, named as Fuchsian Schottky group of arbitrary finite rank, in the context of the classical Schottky group (i.e., Schottky curves which are Euclidean circles). After that, we initiated the construction of the generalized Fuchsian Schottky group of any finite rank by including orientation-reversing isometries of the hyperbolic plane as side-pairing transformations. Further, we have investigated the hyperbolic ends for any arbitrary finite rank Fuchsian Schottky groups from the point of view of the Euler characteristic in the hyperbolic surface. Finally, we have shown that the compact core of the conformally compact Riemann surface can be decomposed into non-tight pairs of pants by using suitable twist parameters with some fixed Bers' constant. The Fenchel-Nielsen coordinates for Teichmüller space corresponding to any finite rank Fuchsian Schottky groups are also obtained.

math.DG↗

arXiv2023

Non-classical generating sets in Fuchsian Schottky groups

The goal of this article is to initiate the study of estimates of the non-classical Schottky structure in the discrete subgroups of the projective special linear group over the real numbers degree $2$. In fact, in this paper, we have investigated the non-classical generating sets in the Fuchsian Schottky groups on the hyperbolic plane with boundary. A Schottky group is usually considered non-classical if the curves used in the Schottky construction are Jordan curves (except the Euclidean circles). More precisely, in this manuscript, we have provided a structure of the rank $2$ Fuchsian Schottky groups with non-classical generating sets by utilizing two suitable hyperbolic M\"obius transformations on the upper-half plane model. In particular, we have derived two non-trivial examples of Fuchsian Schottky groups with non-classical generating sets in the upper-half plane with the circle at infinity as the boundary.

math.DG↗