Bergman kernel asymptotics for singular metrics on punctured Riemann surfaces

Dan Coman, Semyon Klevtsov, George Marinescu

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)593-628
Number of pages36
JournalIndiana University Mathematics Journal
Volume68
Issue number2
DOIs
StatePublished - Jan 1 2019

Keywords

  • Bergman kernel function
  • Quantum Hall effect
  • Singular Hermitian metric

ASJC Scopus subject areas

  • Mathematics(all)

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