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.
|Title of host publication||Number Theory, Analysis and Geometry|
|Subtitle of host publication||In Memory of Serge Lang|
|Number of pages||8|
|State||Published - Mar 1 2012|
Bibliographical notePublisher Copyright:
© Springer Science+Business Media, LLC 2012. All rights reserved.
- harmonic differentials
- non-compact Riemann surfaces
ASJC Scopus subject areas
- Mathematics (all)