scholarly journals Duality of positive currents and plurisubharmonic functions in calibrated geometry

2009 ◽  
Vol 131 (5) ◽  
pp. 1211-1239 ◽  
Author(s):  
F. Reese Harvey ◽  
H. Blaine Lawson Jr.
Keyword(s):  
Plurisubharmonic Functions ◽  
Positive Currents ◽  
Calibrated Geometry

scholarly journals A comparison of positivity in complex and tropical toric geometry

2021 ◽  
Author(s):  
José Ignacio Burgos Gil ◽  
Walter Gubler ◽  
Philipp Jell ◽  
Klaus Künnemann
Keyword(s):  
Toric Variety ◽  
Subsequent Paper ◽  
Toric Geometry ◽  
Plurisubharmonic Functions ◽  
Smooth Complex ◽  
Positive Currents ◽  
Complex Forms ◽  
Correspondence Theorem

AbstractGiven a smooth complex toric variety we will compare real Lagerberg forms and currents on its tropicalization with invariant complex forms and currents on the toric variety. Our main result is a correspondence theorem which identifies the cone of invariant closed positive currents on the complex toric variety with closed positive currents on the tropicalization. In a subsequent paper, this correspondence will be used to develop a Bedford–Taylor theory of plurisubharmonic functions on the tropicalization.

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.

Minimum Principle for Plurisubharmonic Functions and Related Topics

2018 ◽  
Vol 34 (8) ◽  
pp. 1278-1288
Author(s):  
Fu Sheng Deng ◽  
Hui Ping Zhang ◽  
Xiang Yu Zhou
Keyword(s):  
Minimum Principle ◽  
Plurisubharmonic Functions

scholarly journals Differential Tests for Plurisubharmonic Functions and Koch Curves

2018 ◽  
Vol 50 (3) ◽  
pp. 381-400 ◽  
Author(s):  
Sławomir Dinew ◽  
żywomir Dinew
Keyword(s):  
Plurisubharmonic Functions
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