  In the paper we generalize the notion of problem (P) introduced by Poletsky.
We introduce the notion of (P_m) extremals. For example, geodesics are (P_1)
extremals. Using obtained results we present a description of (P_m) 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.
