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Proper holomorphic mappings vs. peak points and Shilov boundary

Łukasz KosińskiWłodzimierz 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.

Lempert theorem for strongly linearly convex domains

Łukasz KosińskiTomasz Warszawski — 2013

Annales Polonici Mathematici

In 1984 L. Lempert showed that the Lempert function and the Carathéodory distance coincide on non-planar bounded strongly linearly convex domains with real-analytic boundaries. Following his paper, we present a slightly modified and more detailed version of the proof. Moreover, the Lempert Theorem is proved for non-planar bounded strongly linearly convex domains.

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