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

Volume 98 / 2010

Włodzimierz Zwonek Annales Polonici Mathematici 98 (2010), 291-299 MSC: Primary 32F45; Secondary 32A36, 30C40. DOI: 10.4064/ap98-3-8

Abstract

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 $-\infty $.

Authors

  • Włodzimierz ZwonekInstytut Matematyki
    Uniwersytet Jagielloński
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail

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