Divergent integrals, residues of Dolbeault forms, and asymptotic Riemann mappings

2016/02/08 by Felder, Giovanni, Kazhdan, David
#30C35 (Secondary) #32C30 #32C35 (Primary) #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1602.02738

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.

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