Hyperbolic Type Geometries in Subdomains

This Licentiate thesis deals with hyperbolic type geometries in planar subdomains. It is known that hyperbolic type distance is always greater in a subdomain than in the original domain. In this work we obtain certain lower estimates for hyperbolic type distances in subdomains in terms of hyperbolic type distances of the original domains. In particular the domains that we consider are cyclic polygons and their circumcircles, sectors and supercircles.