Displaying similar documents to “On the Hausdorff measures associated to the Carathéodory and Kobayashi metrics”

Finsler metrics with propierties of the Kobayashi metric on convex domains.

Myung-Yull Pang (1992)

Publicacions Matemàtiques

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The structure of complex Finsler manifolds is studied when the Finsler metric has the property of the Kobayashi metric on convex domains: (real) geodesics locally extend to complex curves (extremal disks). It is shown that this property of the Finsler metric induces a complex foliation of the cotangent space closely related to geodesics. Each geodesic of the metric is then shown to have a unique extension to a maximal totally geodesic complex curve Σ which has properties of extremal...

Injective hyperbolicity of domains

Marius Overholt (1995)

Annales Polonici Mathematici

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The pseudometric of Hahn is identical to the Kobayashi-Royden pseudometric on domains of dimension greater than two. Thus injective hyperbolicity coincides with ordinary hyperbolicity in this case.

Barbilian's metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics

Wladimir G. Boskoff, Bogdan D. Suceavă (2008)

Czechoslovak Mathematical Journal

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In the present paper we answer two questions raised by Barbilian in 1960. First, we study how far can the hypothesis of Barbilian's metrization procedure can be relaxed. Then, we prove that Barbilian's metrization procedure in the plane generates either Riemannian metrics or Lagrance generalized metrics not reducible to Finslerian or Langrangian metrics.

Concave domains with trivial biholomorphic invariants

Witold Jarnicki, Nikolai Nikolov (2002)

Annales Polonici Mathematici

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It is proved that if F is a convex closed set in ℂⁿ, n ≥2, containing at most one (n-1)-dimensional complex hyperplane, then the Kobayashi metric and the Lempert function of ℂⁿ∖ F identically vanish.