The Journal of Geometric Analysis

, Volume 29, Issue 1, pp 936–956 | Cite as

The Long-Time Behavior of Modified Calabi Flow

  • Xishen Jin
  • Jiawei LiuEmail author


In this paper, we study the long-time behavior of modified Calabi flow to study the existence of generalized Kähler–Ricci soliton. We first give a new expression of the modified K-energy and prove its convexity along weak geodesics. Then we extend this functional to some finite energy spaces. After that, we study the long-time behavior of modified Calabi flow.


Generalized Kähler–Ricci soliton Modified Calabi flow Modified K-energy 

Mathematics Subject Classification

53C55 32W20 



Xishen Jin and Jiawei Liu would like to thank their advisors Professor Jiayu Li and Professor Xi Zhang for their useful conversations and constant encouragement. They also would like to express their gratitude towards Professor Tamás Darvas and Professor Chinh H. Lu for their detailed answers about their paper [4]. They are very grateful to the referee for carefully reading the original manuscript and pointing out some typos. The first author also would like to thank Professor Gang Tian for his encouragement, and the second author also thanks Professor Miles Simon and Xiaohua Zhu for their constant help. The second author was supported by the Program SPP2026 from the German Research Foundation (DFG).


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Authors and Affiliations

  1. 1.Beijing International Center for Mathematical ResearchPeking UniversityBeijingChina
  2. 2.Institut für Analysis und NumerikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

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