Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Differentiability Of The Liouville Map Via Geodesic Currents, Xinlong Dong
Differentiability Of The Liouville Map Via Geodesic Currents, Xinlong Dong
Dissertations, Theses, and Capstone Projects
For a conformally hyperbolic Riemann surface, the Teichmüller space is the space of quasiconformal maps factored by an equivalence relation, and it is a complex Banach manifold. The space of geodesic currents endowed with the uniform weak* topology is a subset of a Fréchet space of Hölder distributions. We introduce an appropriate topology on the space of Hölder distributions and this new topology coincides with the uniform weak* topology on the space of geodesic currents. The Liouville map of the Teichmüller space becomes differentiable in the Fréchet sense. In particular, the derivative of Liouville currents exists and belongs to the …
Growth Of Conjugacy Classes Of Reciprocal Words In Triangle Groups, Blanca T. Marmolejo
Growth Of Conjugacy Classes Of Reciprocal Words In Triangle Groups, Blanca T. Marmolejo
Dissertations, Theses, and Capstone Projects
In this thesis we obtain the growth rates for conjugacy classes of reciprocal words for triangle groups of the form G = Z2 ∗ H where H is finitely generated and does not contain an order 2 element. We explore cases where H is infinite cyclic and finite cyclic. The quotient O = H/G is an orbifold and contains a cone point of order 2, due to the first factor Z2 in the free product G. The reciprocal words in G correspond to geodesics on O which pass through the order 2 cone point on O. We use methods from …