2018/07/03 by Hiroshige Shiga, Shiga, Hiroshige · 1 citation
Mathematics · Biochemistry, Genetics and Molecular Biology · #Analytic and geometric function theory #Bone Metabolism and Diseases #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1807.01096
In the theory of Teichmüller space of Riemann surfaces, we consider the set of Riemann surfaces which are quasiconformally equivalent. For topologically finite Riemann surfaces, it is quite easy to examine if they are quasiconformally equivalent or not. On the other hand, for Riemann surfaces of topologically infinite type, the situation is rather complicated. In this paper, after constructing an example which shows the complexity of the problem, we give some geometric conditions for Riemann surfaces to be quasiconformally equivalent. Our argument enables us to obtain the universal Schottky space which contains all Schottky spaces, the deformation spaces of Schottky groups as the universal Teichmüller space contains all Teichmüller spaces.