Harmonic representatives for cuspidal cohomology classes. (English) Zbl 1250.30037
Goldfeld, Dorian (ed.) et al., Number theory, analysis and geometry. In memory of Serge Lang. Berlin: Springer (ISBN 978-1-4614-1259-5/hbk; 978-1-4614-1260-1/ebook). 161-168 (2012).
Summary: 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.
For the entire collection see [Zbl 1230.00036].
For the entire collection see [Zbl 1230.00036].
MSC:
| 30F30 | Differentials on Riemann surfaces |
| 58J60 | Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) |
