A cup product lemma for continuous plurisubharmonic functions
Complex Variables
2017-04-24 v1
Abstract
A version of Gromov's cup product lemma in which one factor is the (1,0)-part of the differential of a continuous plurisubharmonic function is obtained. As an application, it is shown that a connected noncompact complete Kaehler manifold that has exactly one end and admits a continuous plurisubharmonic function that is strictly plurisubharmonic along some germ of a 2-dimensional complex analytic set at some point has the Bochner-Hartogs property; that is, the first compactly supported cohomology with values in the structure sheaf vanishes.
Cite
@article{arxiv.1704.06496,
title = {A cup product lemma for continuous plurisubharmonic functions},
author = {Terrence Napier and Mohan Ramachandran},
journal= {arXiv preprint arXiv:1704.06496},
year = {2017}
}