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Elementary construction of subharmonic exhaustion functions

Terrence Napier·Mohan Ramachandran
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Abstract

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.

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Terrence Napier, Mohan Ramachandran. 2004-05-27. Elementary construction of subharmonic exhaustion functions. https://arxiv.org/abs/math/0405533

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