scholarly journals A non-integrated defect relation and the uniqueness theorem for meromorphic maps of a complete Kähler manifold into Pn(C)

2013 ◽  
Vol 398 (2) ◽  
pp. 567-581 ◽  
Author(s):  
Qiming Yan
Keyword(s):  
Uniqueness Theorem ◽  
Kähler Manifold ◽  
Defect Relation ◽  
Kahler Manifold ◽  
Meromorphic Maps ◽  
The Uniqueness Theorem ◽  
Complete Kähler Manifold

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 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.

scholarly journals ON THE DYNAMICAL DEGREES OF MEROMORPHIC MAPS PRESERVING A FIBRATION

2012 ◽  
Vol 14 (06) ◽  
pp. 1250042 ◽  
Author(s):  
TIEN-CUONG DINH ◽  
VIÊT-ANH NGUYÊN ◽  
TUYEN TRUNG TRUONG
Keyword(s):  
Dynamical System ◽  
Kähler Manifold ◽  
Kahler Manifold ◽  
Meromorphic Maps ◽  
Dynamical Degrees ◽  
Compact Kähler Manifold

Let f be a dominant meromorphic self-map on a compact Kähler manifold X which preserves a meromorphic fibration π : X → Y of X over a compact Kähler manifold Y. We compute the dynamical degrees of f in terms of its dynamical degrees relative to the fibration and the dynamical degrees of the map g : Y → Y induced by f. We derive from this result new properties of some fibrations intrinsically associated to X when this manifold admits an interesting dynamical system.

scholarly journals A Liouville Property of Holomorphic Maps

2013 ◽  
Vol 2013 ◽  
pp. 1-3
Author(s):  
Chengjie Yu
Keyword(s):  
Sectional Curvature ◽  
Kähler Manifold ◽  
Holomorphic Maps ◽  
Liouville Property ◽  
Bisectional Curvature ◽  
Holomorphic Bisectional Curvature ◽  
Kahler Manifold ◽  
Simply Connected ◽  
Complete Kähler Manifold

We prove a Liouville property of holomorphic maps from a complete Kähler manifold with nonnegative holomorphic bisectional curvature to a complete simply connected Kähler manifold with a certain assumption on the sectional curvature.

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