Function theory on the Neile parabola

Details Function theory on the Neile parabola Function theory on the Neile parabola

2005-12-20

arxiv.org/abs/math/0512473v2

Mathematics

Complex Variables

19 pages. Minor error corrected in theorem 4.2

Scientific paper

We give a formula for the Caratheodory distance on the Neile parabola, the variety {z^2=w^3} restricted to the bidisk; thus making it the first variety with a singularity to have its Caratheodory distance explicitly computed. In addition, we relate this to a mixed Caratheodory-Pick interpolation problem for which known interpolation theorems do not apply. Finally, we prove a bounded holomorphic function extension result from the Neile parabola to the bidisk.

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