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 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 Relative non-pluripolar product of currents

2021 ◽  
Author(s):  
Duc-Viet Vu
Keyword(s):  
Kähler Manifold ◽  
Monotonicity Property ◽  
Necessary Condition ◽  
Positive Current ◽  
Lelong Numbers ◽  
Kahler Manifold ◽  
Closed Positive Current ◽  
Positive Currents ◽  
Compact Kähler Manifold

AbstractLet X be a compact Kähler manifold. Let $$T_1, \ldots , T_m$$ T 1 , … , T m be closed positive currents of bi-degree (1, 1) on X and T an arbitrary closed positive current on X. We introduce the non-pluripolar product relative to T of $$T_1, \ldots , T_m$$ T 1 , … , T m . We recover the well-known non-pluripolar product of $$T_1, \ldots , T_m$$ T 1 , … , T m when T is the current of integration along X. Our main results are a monotonicity property of relative non-pluripolar products, a necessary condition for currents to be of relative full mass intersection in terms of Lelong numbers, and the convexity of weighted classes of currents of relative full mass intersection. The former two results are new even when T is the current of integration along X.

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