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Peak points for domains in ℂⁿ

Armen Edigarian (2015)

Annales Polonici Mathematici

We give a necessary and sufficient condition for the existence of a weak peak function by using Jensen type measures. We also show the existence of a weak peak function for a class of Reinhardt domains.

Poisson geometry and deformation quantization near a strictly pseudoconvex boundary

Eric Leichtnam, Xiang Tang, Alan Weinstein (2007)

Journal of the European Mathematical Society

Let X be a complex manifold with strongly pseudoconvex boundary M . If ψ is a defining function for M , then log ψ is plurisubharmonic on a neighborhood of M in X , and the (real) 2-form σ = i ¯ ( log ψ ) is a symplectic structure on the complement of M in a neighborhood of M in X ; it blows up along M . The Poisson structure obtained by inverting σ extends smoothly across M and determines a contact structure on M which is the same as the one induced by the complex structure. When M is compact, the Poisson structure near...

Proper holomorphic mappings vs. peak points and Shilov boundary

Łukasz Kosiński, Włodzimierz Zwonek (2013)

Annales Polonici Mathematici

We present a result on the existence of some kind of peak functions for ℂ-convex domains and for the symmetrized polydisc. Then we apply the latter result to show the equivariance of the set of peak points for A(D) under proper holomorphic mappings. Additionally, we present a description of the set of peak points in the class of bounded pseudoconvex Reinhardt domains.

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