scholarly journals A cup product lemma for continuous plurisubharmonic functions

2018 ◽  
Vol 10 (02) ◽  
pp. 263-287
Author(s):  
Terrence Napier ◽  
Mohan Ramachandran
Keyword(s):  
Plurisubharmonic Function ◽  
Kähler Manifold ◽  
Analytic Set ◽  
Plurisubharmonic Functions ◽  
Structure Sheaf ◽  
Compactly Supported ◽  
Cup Product ◽  
Kahler Manifold ◽  
Complete Kähler Manifold

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 [Formula: see text]-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.

On uniqueness of meromorphic mappings from complete Kähler manifold into ℙn(ℂ)

2020 ◽  
pp. 2150061
Author(s):  
Ha Huong Giang ◽  
Nguyen Thi Nhung
Keyword(s):  
Uniqueness Theorem ◽  
General Condition ◽  
General Position ◽  
Kähler Manifold ◽  
Meromorphic Mappings ◽  
Kahler Manifold ◽  
Complete Kähler Manifold

In this paper, we prove a uniqueness theorem for meromorphic mappings of a complete Kähler manifold [Formula: see text] into [Formula: see text] sharing hyperplanes in general position under a general condition that the codimension of the intersection of inverse images of any [Formula: see text] hyperplanes is at least two.

Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space

2020 ◽  
Vol 70 (4) ◽  
pp. 863-876
Author(s):  
Ha Huong Giang
Keyword(s):  
Projective Space ◽  
General Condition ◽  
General Position ◽  
Kähler Manifold ◽  
Uniqueness Problem ◽  
Uniqueness Theorems ◽  
Meromorphic Mappings ◽  
Kahler Manifold ◽  
Complete Kähler Manifold

AbstractIn this article, we prove a new generalization of uniqueness theorems for meromorphic mappings of a complete Kähler manifold M into ℙn(ℂ) sharing hyperplanes in general position with a general condition on the intersections of the inverse images of these hyperplanes.

scholarly journals Bounded p.s.h. functions and pseudoconvexity in Kähler manifold

1998 ◽  
Vol 149 ◽  
pp. 1-8 ◽  
Author(s):  
Takeo Ohsawa ◽  
Nessim Sibony
Keyword(s):  
Kähler Manifold ◽  
Pseudoconvex Domains ◽  
Real Hypersurfaces ◽  
Plurisubharmonic Functions ◽  
Kahler Manifold

Abstract.It is proved that the C2-smoothly bounded pseudoconvex domains in Pn admit bounded plurisubharmonic exhaustion functions. Further arguments are given concerning the question of existence of strictly plurisubharmonic functions on neighbourhoods of real hypersurfaces in Pn.

scholarly journals L2 CASTELNUOVO–DE FRANCHIS, THE CUP PRODUCT LEMMA, AND FILTERED ENDS OF KÄHLER MANIFOLDS

2009 ◽  
Vol 01 (01) ◽  
pp. 29-64 ◽  
Author(s):  
TERRENCE NAPIER ◽  
MOHAN RAMACHANDRAN
Keyword(s):  
Riemann Surface ◽  
Holomorphic Mapping ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Proper Holomorphic Mapping ◽  
Bounded Geometry ◽  
Cup Product ◽  
Linearly Independent ◽  
Complete Kähler Manifold

Simple approaches to the proofs of the L2 Castelnuovo–de Franchis theorem and the cup product lemma which give new versions are developed. For example, assume that ω1 and ω2 are two linearly independent closed holomorphic 1-forms on a bounded geometry connected complete Kähler manifold X with ω2 in L2. According to a version of the L2 Castelnuovo–de Franchis theorem obtained in this paper, if ω1 ∧ ω2 ≡ 0, then there exists a surjective proper holomorphic mapping of X onto a Riemann surface for which ω1 and ω2 are pull-backs. Previous versions required both forms to be in L2.

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