On extremal mappings in complex ellipsoids
Armen Edigarian
Abstract
In the paper we generalize the notion of problem (P) introduced by Poletsky. We introduce the notion of (Pm) extremals. For example, geodesics are (P1) extremals. Using obtained results we present a description of (Pm) extremals in arbitrary complex ellipsoids. It is a generalization of the result obtained by Jarnicki-Pflug-Zeinstra. We also have a proof of conjecture put forward by Pflug-Zwonek concerning the formulas for geodesics in non-convex complex ellipsoids.
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