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Annals of Global Analysis and Geometry

, Volume 55, Issue 2, pp 215–241 | Cite as

Expansions of solutions to extremal metric type equations on blowups of cscK surfaces

  • Ved V. DatarEmail author
Article
  • 27 Downloads

Abstract

The aim of this article is to study expansions of solutions to an extremal metric type equation on the blowup of constant scalar curvature Kähler surfaces. This is related to finding constant scalar curvature Kähler (cscK) metrics on K-stable blowups of extremal Kähler surfaces (Székelyhidi in Duke Math J 161(8):1411–1453, 2012).

Keywords

Extremal metrics Gluing constructions Blowups 

Notes

Acknowledgements

I would like to thank Gábor Székelyhidi for introducing me to Conjecture 1 and for sharing many useful insights. I would also like to thank Claudio Arezzo, Richard Bamler, Rafe Mazzeo, Michael Singer, Jian Song and Xiaowei Wang for stimulating discussions.

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUC BerkeleyBerkeleyUSA

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