Le cône des fonctions plurisousharmoniques négatives et une conjecture de Coman

@article{Carlehed2002LeCD,
  title={Le c{\^o}ne des fonctions plurisousharmoniques n{\'e}gatives et une conjecture de Coman},
  author={Magnus Carlehed and Johannes I. Wiegerinck},
  journal={Annales Polonici Mathematici},
  year={2002},
  volume={80},
  pages={93-108}
}
Les fonctions plurisousharmoniques n'egatives dans un domaine Omega de C^n forment un c^one convexe. Nous consid'erons les points extr'emaux de ce c^one, et donnons trois exemples. En particulier, nous traitons le cas de la fonction de Green pluricomplexe. Nous calculons celle du bidisque, lorsque les p^oles se situent sur un axe. Nous montrons que cette fonction ne se confonde pas avec la fonction de Lempert correspondante. Cela donne un contre-exemple `a une conjecture de Dan Coman. 
Computing the Pluricomplex Green Function with Two Poles
TLDR
Numerical computations of the pluricomplex Green function g with two poles of equal weight for the bidisk strongly suggest that Coman's conjecture holds, that is that g equals the Lempertfunction. Expand
LIMITS OF MULTIPOLE PLURICOMPLEX GREEN FUNCTIONS
Let Ω be a bounded hyperconvex domain in ℂn, 0 ∈ Ω, and Se a family of N poles in Ω, all tending to 0 as e tends to 0. To each Se we associate its vanishing ideal and pluricomplex Green function .Expand
Extreme plurisubharmonic singularities
A plurisubharmonic singularity is extreme if it cannot be represented as the sum of non-homothetic singularities. A complete characterization of such singularities is given for the case ofExpand
Convergence and multiplicities for the Lempert function
Given a domain Ω⊂ℂn, the Lempert function is a functional on the space $\text{Hol}(\mathbb{D},\Omega)$ of analytic disks with values in Ω, depending on a set of poles in Ω. We generalize itsExpand
Green vs. Lempert functions: a minimal example
The Lempert function for a set of poles in a domain of $\mathbb C^n$ at a point $z$ is obtained by taking a certain infimum over all analytic disks going through the poles and the point $z$, andExpand
Three-point Nevanlinna Pick problem in the polydisc
It is very elementary to observe that functions interpolating an extremal two-point Pick problem on the polydisc are just left inverses to complex geodesics. In the present article we show that theExpand
Pluricomplex Green and Lempert functions for equally weighted poles
For $\Omega$ a domain in $\mathbb C^n$, the pluricomplex Green function with poles $a_1, ...,a_N \in \Omega$ is defined as $G(z):=\sup \{u(z): u\in PSH_-(\Omega), u(x)\le \log \|x-a_j\|+C_jExpand
Green versus Lempert functions: A minimal example
The Lempert function for a set of poles in a domain of Cn at a point z is obtained by taking a certain infimum over all analytic disks going through the poles and the point z, and majorizes theExpand
AN EXAMPLE OF LIMIT OF LEMPERT FUNCTIONS
The Lempert function for a set of poles in a domain of C n at a point z is obtained by taking a certain infimum over all analytic disks going through the poles and the point z, and ma- jorizes theExpand
Coman conjecture for the bidisc
In the paper we show the equality between the Lempert function and the Green function with two poles with equal weights in the bidisc thus giving the positive answer to a conjecture of Coman in theExpand
...
1
2
...

References

SHOWING 1-5 OF 5 REFERENCES
La métrique de Kobayashi et la représentation des domaines sur la boule
© Bulletin de la S. M. F., 1981, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accordExpand
The pluricomplex Green function with two poles of the unit ball of ℂn
In this paper we find the formula for the pluricomplex Green function of the unit ball of C n with two poles ofequal weights. The strategy will be to show the existence ofa f tion ofthe ballExpand
Notions of Convexity
The first two chapters of the book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in theExpand
Non-linearity of the pluricomplex Green function
We consider the pluricomplex Green function with multiple poles as introduced by Lelong. We give a partial solution to a question concerning the set where the multipole Green function coincides withExpand
Potential theory in the complex plane
Preface A word about notation 1. Harmonic functions 2. Subharmonic functions 3. Potential theory 4. The Dirichlet problem 5. Capacity 6. Applications Borel measures Bibliography Index Glossary ofExpand