Equlibrium measure of a product subset of ℂⁿ

Błocki, Zbigniew

doi:10.1090/S0002-9939-00-05552-0

Equlibrium measure of a product subset of ${\mathbb {C}}^{n}$
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by Zbigniew Błocki PDF

Proc. Amer. Math. Soc. 128 (2000), 3595-3599 Request permission

Abstract:

In this note we show that an equilibrium measure of a product of two subsets of ${\mathbb {C}}^{n}$ and ${\mathbb {C}}^{m}$, respectively, is a product of their equilibrium measures. We also obtain a formula for $(dd^{c}\max \{u,v\})^{p}$, where $u,v$ are locally bounded plurisubharmonic functions and $2\leq p\leq n$.

References

Eric Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), no. 1-2, 1–40. MR 674165, DOI 10.1007/BF02392348
Eric Bedford and B. A. Taylor, The complex equilibrium measure of a symmetric convex set in $\textbf {R}^n$, Trans. Amer. Math. Soc. 294 (1986), no. 2, 705–717. MR 825731, DOI 10.1090/S0002-9947-1986-0825731-8
Armen Edigarian and Evgeny A. Poletsky, Product property of the relative extremal function, Bull. Polish Acad. Sci. Math. 45 (1997), no. 4, 331–335. MR 1489875
Maciej Klimek, Pluripotential theory, London Mathematical Society Monographs. New Series, vol. 6, The Clarendon Press, Oxford University Press, New York, 1991. Oxford Science Publications. MR 1150978
A. Sadullaev, Plurisubharmonic measures and capacities on complex manifolds, Russian Math. Surveys 36 (1981), 61-119.
Józef Siciak, Extremal plurisubharmonic functions in $\textbf {C}^{n}$, Ann. Polon. Math. 39 (1981), 175–211. MR 617459, DOI 10.4064/ap-39-1-175-211
Shinichi Tajima, Microlocal analysis of tangential systems of Cauchy-Riemann equations, Sūgaku 43 (1991), no. 2, 139–150 (Japanese). MR 1114066