Remarks on Lempert functions of balanced domains

Abstract

This note should clarify how the behavior of certain invariant objects reflects the geometric convexity of balanced domains. h D (z) = inf{t > 0 : z/t ∈ D}, z ∈ C n , 2000 Mathematics Subject Classification. 32F45.

Invariant functions and metrics in complex analysis

“…Remark. Some propositions and examples in the spirit of the above for k (m) can be found in the paper [90] of the author and P. Pflug.…”

“…Chapter 1: in [86,87,88,89,90,103]; Chapter 2: in [82,91,94,95,96,97,100,101,102,104]; Chapter 3: in [57,80,81,83,92,84,98].…”

Invariant functions and metrics in complex analysis

“…The results are published as follows: Chapter 1 -in [86,87,88,89,90,103]; Chapter 2 -in [82,91,94,95,96,97,100,101,102,104]; Chapter 3 -in [55,80,81,83,92,84,98]. Some of the mentioned results are from [79,85,93,99].…”