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Instantaneously complete Chern–Ricci flow and Kähler–Einstein metrics

  • Shaochuang Huang
  • Man-Chun LeeEmail author
  • Luen-Fai Tam
Article
  • 89 Downloads

Abstract

In this work, we obtain some existence results of Chern–Ricci Flows and the corresponding Potential Flows on complex manifolds with possibly incomplete initial data. We discuss the behaviour of the solution as \(t\rightarrow 0\). These results can be viewed as a generalization of an existence result of Ricci flow by Giesen and Topping for surfaces of hyperbolic type to higher dimensions in certain sense. On the other hand, we also discuss the long time behaviour of the solution and obtain some sufficient conditions for the existence of Kähler-Einstein metric on complete non-compact Hermitian manifolds, which generalizes the work of Lott–Zhang and Tosatti–Weinkove to complete non-compact Hermitian manifolds with possibly unbounded curvature.

Mathematics Subject Classification

Primary 32Q15 Secondary 53C44 

Notes

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Copyright information

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

Authors and Affiliations

  1. 1.Yau Mathematical Sciences CenterTsinghua UniversityBeijingChina
  2. 2.Department of MathematicsNorthwestern UniversityEvanstonUSA
  3. 3.The Institute of Mathematical Sciences and Department of MathematicsThe Chinese University of Hong KongShatinChina

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