 

Luca Fabrizio Di Cerbo
SeibergWitten equations on certain manifolds with cusps view print


Published: 
August 13, 2011 
Keywords: 
SeibergWitten equations, finitevolume Einstein metrics 
Subject: 
53C21 


Abstract
We study the SeibergWitten equations on noncompact manifolds diffeomorphic to the product of two hyperbolic Riemann surfaces.
First, we show how to construct irreducible solutions of the
SeibergWitten equations for any metric of finite volume which has a
"nice'' behavior at infinity. Then we compute the infimum of the
L^{2}norm of scalar curvature on these spaces and give
nonexistence results for Einstein metrics on blowups. This
generalizes to the finite volume setting some wellknown results of
LeBrun.


Acknowledgements
This work has been partially supported by the Simons Foundation.


Author information
Mathematics Department, Duke University, Box 90320, Durham, NC 27708, USA
luca@math.duke.edu

