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The Kobayashi metric for non-convex complex ellipsoids

Peter Pflug·Wlodzimierz Zwonek
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Abstract

In the paper we give some necessary conditions for a mapping to be a $κ$-geodesic in non-convex complex ellipsoids. Using these results we calculate explicitly the Kobayashi metric in the ellipsoids $\{|z_1|^2+|z_2|^{2m}<1\}\subset\bold C^2$, where $m<\frac12$.

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Peter Pflug, Wlodzimierz Zwonek. 1994-07-31. The Kobayashi metric for non-convex complex ellipsoids. https://arxiv.org/abs/math/9407201

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