Function theory on the Neil parabola

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

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