Mathematics – Differential Geometry
Scientific paper
2004-05-27
Mathematics
Differential Geometry
Scientific paper
By a theorem of Greene and Wu, a noncompact connected Riemannian manifold admits a smooth strictly subharmonic exhaustion function. Demailly provided an elementary proof of this fact. A further simplification of Demailly's proof and some (mostly known) applications are described. Applications include the fact that the holomorphic line bundle associated to a nontrivial effective divisor on a compact connected complex manifold admits a smooth Hermitian metric with positive scalar curvature.
Napier Terrence
Ramachandran Mohan
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