Geometry of symmetrized ellipsoids.
Invariant Functions on Neil Parabola in Cn
2000 Mathematics Subject Classification: Primary 32F45. We present the Carathéodory and the inner Caratheodory distances and the Carathéodory-Reiffen metric on generalized Neil parabolas in Cn. It is a generalization of the results from [4] and [5]. This work is a part of the Research Grant No. 1 PO3A 005 28, which is supported by public means in the programme promoting science in Poland in the years 2005–2008.
Inner -th Carathéodory-Reiffen completeness of Reinhardt domains
A description of bounded pseudoconvex Reinhardt domains, which are complete with respect to the inner -th Carathéodory-Reiffen distance, is given.
Completeness of the inner kth Reiffen pseudometric
We give an example of a Zalcman-type domain in ℂ which is complete with respect to the integrated form of the (k+1)st Reiffen pseudometric, but not complete with respect to the kth one.
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