On extremal mappings in complex ellipsoids

1995/03/30 by Armen Edigarian, Edigarian, Armen
Mathematics · #32 #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Equations Stability Results #math.CV #msc:32

paper · pdf · doi:10.48550/arxiv.math/9503201

arxiv created 1995/03/30 · openalex publication_date 1995/03/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 (P₁) 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.

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