New York Journal of Mathematics
Volume 17 (2011) 491-512


Luca Fabrizio Di Cerbo

Seiberg-Witten equations on certain manifolds with cusps

view    print

Published: August 13, 2011
Keywords: Seiberg-Witten equations, finite-volume Einstein metrics
Subject: 53C21

We study the Seiberg-Witten equations on noncompact manifolds diffeomorphic to the product of two hyperbolic Riemann surfaces. First, we show how to construct irreducible solutions of the Seiberg-Witten equations for any metric of finite volume which has a "nice'' behavior at infinity. Then we compute the infimum of the L2-norm of scalar curvature on these spaces and give nonexistence results for Einstein metrics on blow-ups. This generalizes to the finite volume setting some well-known results of LeBrun.


This work has been partially supported by the Simons Foundation.

Author information

Mathematics Department, Duke University, Box 90320, Durham, NC 27708, USA