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Subjects
30-XX Functions of a complex variable
30Hxx Spaces and algebras of analytic functions
30H20 Bergman spaces, Fock spaces

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An example for the holomorphic sectional curvature of the Bergman metric

Żywomir Dinew (2010)

Annales Polonici Mathematici

We study the behaviour of the holomorphic sectional curvature (or Gaussian curvature) of the Bergman metric of planar annuli. The results are then utilized to construct a domain for which the curvature is divergent at one of its boundary points and moreover the upper limit of the curvature at that point is maximal possible, equal to 2, whereas the lower limit is -∞.

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

Włodzimierz Zwonek (2010)

Annales Polonici Mathematici

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 -∞ .

Currently displaying 1 – 2 of 2

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