scholarly journals Polynomial hulls and positive currents

2003 ◽  
Vol 12 (3) ◽  
pp. 317-334 ◽  
Author(s):  
Tien-Cuong Dinh ◽  
Mark G. Lawrence
Keyword(s):  
Positive Currents ◽  
Polynomial Hulls

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.

Polynomial hulls and $H^\infty$ control for a hypoconvex constraint

2000 ◽  
Vol 317 (4) ◽  
pp. 677-701 ◽  
Author(s):  
Marshall A. Whittlesey
Keyword(s):  
Polynomial Hulls

Polynomial hulls and analytic discs

2017 ◽  
Vol 145 (10) ◽  
pp. 4443-4448
Author(s):  
Egmont Porten
Keyword(s):  
Analytic Discs ◽  
Polynomial Hulls

scholarly journals Polynomial hulls and an optimization problem

2004 ◽  
Vol 14 (3) ◽  
pp. 545-556
Author(s):  
Marshall A. Whittlesey
Keyword(s):  
Optimization Problem ◽  
Polynomial Hulls

scholarly journals Dimension of ergodic measures and currents on

2019 ◽  
Vol 40 (8) ◽  
pp. 2131-2155
Author(s):  
CHRISTOPHE DUPONT ◽  
AXEL ROGUE
Keyword(s):  
Upper Bound ◽  
Equilibrium Measure ◽  
Pointwise Dimension ◽  
Ergodic Measures ◽  
Positive Currents ◽  
Green Current

Let $f$ be a holomorphic endomorphism of $\mathbb{P}^{2}$ of degree $d\geq 2$. We estimate the local directional dimensions of closed positive currents $S$ with respect to ergodic dilating measures $\unicode[STIX]{x1D708}$. We infer several applications. The first one is an upper bound for the lower pointwise dimension of the equilibrium measure, towards a Binder–DeMarco’s formula for this dimension. The second one shows that every current $S$ containing a measure of entropy $h_{\unicode[STIX]{x1D708}}>\log d$ has a directional dimension ${>}2$, which answers a question of de Thélin–Vigny in a directional way. The last one estimates the dimensions of the Green current of Dujardin’s semi-extremal endomorphisms.

Electrical Stimulation of the Ear: Clinical Applications

1983 ◽  
Vol 92 (6) ◽  
pp. 621-622 ◽  
Author(s):  
M. Portmann ◽  
J.-M. Aran ◽  
M. Nègrevergne ◽  
Y. Cazals
Keyword(s):  
Electrical Stimulation ◽  
Round Window ◽  
Clinical Applications ◽  
Positive Currents ◽  
Stimulation Of

Electrical stimulation of the ear in humans was performed with an extracochlear electrode on the round window. With positive currents, suppression of tinnitus could be induced. With negative currents, auditory sensations were evoked. Since electrical stimulation with DC currents may be hazardous in the long term, it cannot yet be proposed for the suppression of tinnitus. However, electrically evoked hearing sensations with AC currents seem to be of definite interest for some totally deaf patients.

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