Elementary construction of subharmonic exhaustion functions
Differential Geometry
2007-05-23 v1
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.
Cite
@article{arxiv.math/0405533,
title = {Elementary construction of subharmonic exhaustion functions},
author = {Terrence Napier and Mohan Ramachandran},
journal= {arXiv preprint arXiv:math/0405533},
year = {2007}
}