Divergent integrals, residues of dolbeault forms, and asymptotic riemann mappings

Giovanni Felder; David Kazhdan

doi:10.1093/imrn/rnw190

Divergent integrals, residues of dolbeault forms, and asymptotic riemann mappings

Giovanni Felder^*
, David Kazhdan

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We describe the asymptotic behaviour and the dependence on the regularization of logarithmically divergent integrals of products of meromorphic and antimeromorphic forms on complex manifolds. Our formula is expressed in terms of residues of Dolbeault forms, a notion introduced in this paper. The proof is based on a result on the asymptotic behaviour of Riemann mappings of small domains.

Original language	English
Pages (from-to)	5897-5918
Number of pages	22
Journal	International Mathematics Research Notices
Volume	2017
Issue number	19
DOIs	https://doi.org/10.1093/imrn/rnw190
State	Published - 1 Oct 2017

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© The Author(s) 2016. Published by Oxford University Press. All rights reserved.

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AB - We describe the asymptotic behaviour and the dependence on the regularization of logarithmically divergent integrals of products of meromorphic and antimeromorphic forms on complex manifolds. Our formula is expressed in terms of residues of Dolbeault forms, a notion introduced in this paper. The proof is based on a result on the asymptotic behaviour of Riemann mappings of small domains.

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Divergent integrals, residues of dolbeault forms, and asymptotic riemann mappings

Abstract

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