Annals of Global Analysis and Geometry

, Volume 41, Issue 3, pp 371–380 | Cite as

Finite-volume complex surfaces without cuspidal Einstein metrics

Article

Abstract

We derive an obstruction to the existence of cuspidal Einstein metrics on finite-volume complex surfaces. This generalizes a theorem of LeBrun for compact complex surfaces. As in the compact case, such a result relies on a scalar curvature estimate. Finally, the obstruction is made explicit on some examples.

Keywords

Seiberg–Witten equations Finite-volume Einstein metrics Scalar curvature 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentDuke UniversityDurhamUSA

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