Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • Some estimates for the Bergman Kernel and Metric in Terms of Logarithmic Capacity

  • Zbigniew Błocki
  • Journal:
    Nagoya Mathematical Journal / Volume 185 / 2007
    Published online by Cambridge University Press:
    11 January 2016, pp. 143-150
    Print publication:
    2007
    • Article
      • You have access
    • PDF
    • Export citation

  • For a bounded domain Ω on the plane we show the inequality cΩ (z)2 ≤ 2πKΩ (z), z ∈ Ω, where cΩ (z) is the logarithmic capacity of the complement ℂ\Ω with respect to z and KΩ is the Bergman kernel. We thus improve a constant in an estimate due to T. Ohsawa but fall short of the inequality cΩ (z)2 ≤ πKΩ (z) conjectured by N. Suita. The main tool we use is a comparison, due to B. Berndtsson, of the kernels for the weighted complex Laplacian and the Green function. We also show a similar estimate for the Bergman metric and analogous results in several variables.

  • Bounds on canonical Green's functions

  • J. Jorgenson, J. Kramer
  • Journal:
    Compositio Mathematica / Volume 142 / Issue 3 / May 2006
    Published online by Cambridge University Press:
    17 May 2006, pp. 679-700
    Print publication:
    May 2006
    • Article
      • You have access
    • PDF
    • Export citation

  • A fundamental object in the theory of arithmetic surfaces is the Green's function associated to the canonical metric. Previous expressions for the canonical Green's function have relied on general functional analysis or, when using specific properties of the canonical metric, the classical Riemann theta function. In this article, we derive a new identity for the canonical Green's function involving the hyperbolic heat kernel. As an application of our results, we obtain bounds for the canonical Green's function through covers and for families of modular curves.