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arXiv · 1704.06496

A cup product lemma for continuous plurisubharmonic functions

Terrence Napier·Mohan Ramachandran
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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.

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Terrence Napier, Mohan Ramachandran. 2017-04-21. A cup product lemma for continuous plurisubharmonic functions. https://doi.org/10.1142/s1793525318500085

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