Harmonic representatives for cuspidal cohomology classes

  • Józef Dodziuk
  • Jeffrey McGowan
  • Peter Perry


We give a construction of harmonic differentials that uniquely represent cohomology classes of a non-compact Riemann surface of finite topology. We construct these differentials by cutting off all cusps along horocycles and solving a suitable boundary value problem on the truncated surface. We then pass to the limit as the horocycle in each cusp recedes to infinity.

Key words

harmonic differentials non-compact Riemann surfaces 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.PHD Program in MathematicsGrad School and University Center (CUNY)New YorkUSA
  2. 2.Department of Mathematical SciencesCentral Connecticut State UniversityNew BritainUSA
  3. 3.Department of MathematicsUniversity of KentuckyLexingtonUSA

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