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Analysis and Mathematical Physics

, Volume 8, Issue 3, pp 383–414 | Cite as

Comments on the Green’s function of a planar domain

  • Diganta Borah
  • Pranav Haridas
  • Kaushal Verma
Article
  • 191 Downloads

Abstract

We study several quantities associated to the Green’s function of a multiply connected domain in the complex plane. Among them are some intrinsic properties such as geodesics, curvature, and \(L^2\)-cohomology of the capacity metric and critical points of the Green’s function. The principal idea used is an affine scaling of the domain that furnishes quantitative boundary behaviour of the Green’s function and related objects.

Keywords

Green’s function Critical points Capactity metric Geodesics Curvature 

Mathematics Subject Classification

30C40 30F45 31A15 31C15 32F45 32Q05 32Q15 32Q45 34B27 53C22 53C23 

Notes

Acknowledgements

The first named author was supported by the DST-INSPIRE Grant IFA-13 MA-21. The last named author was supported by the DST Swarnajayanti Fellowship 2009–2010 and a UGC–CAS Grant.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Indian Institute of Science Education and Research (IISER)PuneIndia
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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