Journal of Geometric Analysis

, Volume 23, Issue 3, pp 1078–1084 | Cite as

Gunning–Narasimhan’s Theorem with a Growth Condition



Given a compact Riemann surface X and a point x 0X, we construct a holomorphic function without critical points on the punctured Riemann surface R=X\{x 0} which is of finite order at x 0.


Riemann surface Divisor Function of finite order 

Mathematics Subject Classification (2000)

32E10 32E30 32H02 14H05 


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Copyright information

© Mathematica Josephina, Inc. 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Institute of Mathematics, Physics and MechanicsLjubljanaSlovenia
  3. 3.Graduate School of MathematicsNagoya UniversityNagoyaJapan

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