Title: A cup product lemma for continuous plurisubharmonic functions,
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.