A cup product lemma for continuous plurisubharmonic functions

Terrence Napier; Mohan Ramachandran

doi:10.1142/S1793525318500085

A cup product lemma for continuous plurisubharmonic functions

Terrence Napier
, Mohan Ramachandran

Mathematics

Lehigh University

Research output: Contribution to journal › Article › peer-review

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 Kähler 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.

Original language	English
Pages (from-to)	263-287
Number of pages	25
Journal	Journal of Topology and Analysis
Volume	10
Issue number	2
DOIs	https://doi.org/10.1142/S1793525318500085
State	Published - Jun 1 2018

Keywords

Bochner-Hartogs property
Kähler

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10.1142/S1793525318500085

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AB - 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 Kähler 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.

KW - Bochner-Hartogs property

KW - Kähler

UR - https://www.scopus.com/pages/publications/84996866121

U2 - 10.1142/S1793525318500085

DO - 10.1142/S1793525318500085

M3 - Article

AN - SCOPUS:84996866121

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VL - 10

SP - 263

EP - 287

JO - Journal of Topology and Analysis

JF - Journal of Topology and Analysis

IS - 2

ER -

A cup product lemma for continuous plurisubharmonic functions

Abstract

Keywords

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