Expansion formula for complex Monge–Ampère equation along cone singularities

  • Hao YinEmail author
  • Kai Zheng


In this paper, we prove the asymptotic expansion of the solutions to some singular complex Monge–Ampère equation which arise naturally in the study of the conical Kähler–Einstein metric.

Mathematics Subject Classification

35J96 35J75 



The work of H. Yin is supported by NSFC 11471300. The work of K. Zheng has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 703949, and was also partially supported by the Engineering and Physical Sciences Research Council (EPSRC) on a Programme Grant entitled “Singularities of Geometric Partial Differential Equations” reference number EP/K00865X/1.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiChina
  2. 2.School of Mathematical ScienceTongji UniversityShanghaiChina
  3. 3.Mathematics InstituteUniversity of WarwickCoventryUK

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