Harmonic representatives for cuspidal cohomology classes

Józef Dodziuk, Jeffrey McGowan, Peter Perry

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish
Title of host publicationNumber Theory, Analysis and Geometry
Subtitle of host publicationIn Memory of Serge Lang
Pages161-168
Number of pages8
Volume9781461412601
ISBN (Electronic)9781461412601
DOIs
StatePublished - Mar 1 2012

Keywords

  • harmonic differentials
  • non-compact Riemann surfaces

ASJC Scopus subject areas

  • Mathematics (all)

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