Pluripotential Energy

Details Pluripotential Energy Pluripotential Energy

2010-07-14

arxiv.org/abs/1007.2391v1

Mathematics

Complex Variables

Scientific paper

For probability measures $\mu$ on compact subsets of $\CC^n$ we define two functionals $J(\mu)$ and $W(\mu)$ modeled on discrete approximations to $\mu$ and multivariate Vandermonde determinants. We show that these functionals coincide, up to a constant, with the electrostatic energy of $\mu$ defined in a more general setting by Berman, Boucksom, Guedj and Zeriahi. This generalizes the classical notion of logarithmic energy of a measure in the complex plane; i.e., the case $n=1$.

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