On the Darboux equation.
A constant in pluripotential theory
We compute the constant sup : P a polynomial in , where S denotes the euclidean unit sphere in and σ its unitary surface measure.
Singular sets of separately analytic functions
We complete the characterization of singular sets of separately analytic functions. In the case of functions of two variables this was earlier done by J. Saint Raymond and J. Siciak.
The complex Monge-Ampère operator in hyperconvex domains
Weak solutions to the complex Hessian equation
We investigate the class of functions associated with the complex Hessian equation .
A note on the Hörmander, Donnelly-Fefferman, and Berndtsson L²-estimates for the ∂̅-operator
We give upper and lower bounds for constants appearing in the L²-estimates for the ∂̅-operator due to Donnelly-Fefferman and Berndtsson.
On the product property for the transfinite diameter
We give a pluripotential-theoretic proof of the product property for the transfinite diameter originally shown by Bloom and Calvi. The main tool is the Rumely formula expressing the transfinite diameter in terms of the global extremal function.
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