Annali di Matematica Pura ed Applicata (1923 -)

, Volume 198, Issue 1, pp 289–306 | Cite as

Cusp Kähler–Ricci flow on compact Kähler manifolds

  • Jiawei LiuEmail author
  • Xi Zhang


In this paper, we study the limiting flow of conical Kähler–Ricci flows when the cone angles tend to 0. We prove the existence and uniqueness of this limiting flow with cusp singularity on compact Kähler manifold M which carries a smooth hypersurface D such that the twisted canonical bundle \(K_M+D\) is ample. Furthermore, we prove that this limiting flow converge to a unique cusp Kähler–Einstein metric.


Cusp Kähler–Ricci flow Conical Kähler–Ricci flow Cusp Kähler–Einstein metric 

Mathematics Subject Classification

53C55 32W20 



The authors would like to thank Professor Jiayu Li for providing many suggestions. They also would like to express their gratitude toward the referees for their careful reading and valuable suggestions. The first author also would like to thank his postdoctoral advisors Professor Miles Simon and Professor Xiaohua Zhu for their useful discussion and encouragement. The first author is partially supported by SPP2026 from the German Research Foundation (DFG), and the second author is partially supported by NSF in China Nos. 11625106, 11571332 and 11721101.


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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für Analysis und NumerikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany
  2. 2.Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiChina

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