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Displaying similar documents to “Isometries of the Teichmüller metric”

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...

Generalized P-reducible (α,β)-metrics with vanishing S-curvature

A. Tayebi, H. Sadeghi (2015)

Annales Polonici Mathematici

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We study one of the open problems in Finsler geometry presented by Matsumoto-Shimada in 1977, about the existence of a concrete P-reducible metric, i.e. one which is not C-reducible. In order to do this, we study a class of Finsler metrics, called generalized P-reducible metrics, which contains the class of P-reducible metrics. We prove that every generalized P-reducible (α,β)-metric with vanishing S-curvature reduces to a Berwald metric or a C-reducible metric. It follows that there...

Strengthened Moser’s conjecture, geometry of Grunsky coefficients and Fredholm eigenvalues

Samuel Krushkal (2007)

Open Mathematics

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The Grunsky and Teichmüller norms ϰ(f) and k(f) of a holomorphic univalent function f in a finitely connected domain D ∋ ∞ with quasiconformal extension to ℂ ^ are related by ϰ(f) ≤ k(f). In 1985, Jürgen Moser conjectured that any univalent function in the disk Δ* = z: |z| > 1 can be approximated locally uniformly by functions with ϰ(f) < k(f). This conjecture has been recently proved by R. Kühnau and the author. In this paper, we prove that approximation is possible in a stronger...

On isotropic Berwald metrics

Akbar Tayebi, Behzad Najafi (2012)

Annales Polonici Mathematici

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We prove that every isotropic Berwald metric of scalar flag curvature is a Randers metric. We study the relation between an isotropic Berwald metric and a Randers metric which are pointwise projectively related. We show that on constant isotropic Berwald manifolds the notions of R-quadratic and stretch metrics are equivalent. Then we prove that every complete generalized Landsberg manifold with isotropic Berwald curvature reduces to a Berwald manifold. Finally, we study C-conformal changes...

Asymptotic behavior of the sectional curvature of the Bergman metric for annuli

Włodzimierz Zwonek (2010)

Annales Polonici Mathematici

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We extend and simplify results of [Din 2010] where the asymptotic behavior of the holomorphic sectional curvature of the Bergman metric in annuli is studied. Similarly to [Din 2010] the description enables us to construct an infinitely connected planar domain (in our paper it is a Zalcman type domain) for which the supremum of the holomorphic sectional curvature is two, whereas its infimum is equal to -∞ .