Bergman Kernel Asymptotics for Singular Metrics on Punctured Riemann Surfaces

We consider singular metrics on a punctured Riemann surface and on a line bundle, and study the behavior of the Bergman kernel in the neighborhood of the punctures. The results have an interpretation in terms of the asymptotic profile of the density-of-states function of the lowest Landau level in q...

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Bibliographic Details
Published in:Indiana University mathematics journal 2019-01, Vol.68 (2), p.593-628
Main Authors: Coman, Dan, Klevtsov, Semyon, Marinescu, George
Format: Article
Language:English
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Summary:We consider singular metrics on a punctured Riemann surface and on a line bundle, and study the behavior of the Bergman kernel in the neighborhood of the punctures. The results have an interpretation in terms of the asymptotic profile of the density-of-states function of the lowest Landau level in quantum Hall effect.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2019.68.7589