Embedding open Riemann surfaces in Riemannian manifolds



For the Riemann surface of the topological type, we can get a conformai model in orientable Riemannian manifolds. We will prove that there is a conformally equivalent model in orientable Riemannian manifolds for a given open Riemann surface. To end up we utilize Garsia 's Continuity lemma and Brouwer's Fixed Point lemma along with the Teichmüller theory.

Math Subject Classifications


Key Words and Phrases

embedding open Riemann surface Teichmüller space conformai deformation 


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Copyright information

© Mathematica Josephina, Inc. 1999

Authors and Affiliations

  1. 1.Department of Applied Mathematics, College of Natural ScienceKonKuk UniversityChoongbukS. Korea

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