A generalization of Pick's theorem and its applications to intrinsic metrics
A generalization to the Hardy-Sobolev spaces of an - logarithmic type estimate
The main purpose of this article is to give a generalization of the logarithmic-type estimate in the Hardy-Sobolev spaces ; , and is the open unit disk or the annulus of the complex space .
An example for the holomorphic sectional curvature of the Bergman metric
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 -∞.
An Expansion of the L- Kernel Over Domains in the Complex Plane.
An inequality on solutions of heat equation.
Asymptotic behavior of the sectional curvature of the Bergman metric for annuli
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 -∞ .