Holomorphic Structures on Topological Surfaces

  • Terrence Napier
  • Mohan Ramachandran
Part of the Cornerstones book series (COR)


In this chapter, we address the natural problem of determining conditions for a topological surface to admit a holomorphic structure. One necessary condition is, of course, that the surface be orientable. According to Radó’s theorem (Theorem 2.11.1), another necessary condition is that the surface be second countable. It turns out that these two conditions are also sufficient.


Riemann Surface Dirichlet Problem Complex Surface Topological Surface Linear Differential Operator 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsLehigh UniversityBethlehemUSA
  2. 2.Department of MathematicsSUNY at BuffaloBuffaloUSA

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