Mathematische Annalen

, Volume 364, Issue 3–4, pp 777–792 | Cite as

Rotational symmetry of conical Kähler–Ricci solitons

  • Otis ChodoshEmail author
  • Frederick Tsz-Ho Fong


We show that expanding Kähler–Ricci solitons which have positive holomorphic bisectional curvature and are \(C^{2}\)-asymptotic to a conical Kähler manifold at infinity must be the U(n)-rotationally symmetric expanding solitons constructed by Cao.

Mathematics Subject Classification

Primary 53C44 Secondary 35C08 



The first named author was supported in part by a National Science Foundation Graduate Research Fellowship DGE-1147470. He would like to thank Simon Brendle for many discussions concerning his soliton uniqueness results, as well as for his support and encouragement. The second named author would like to thank Richard Schoen, Simon Brendle and Yanir Rubinstein who aroused his interest concerning topics related to this paper when he was a graduate student at Stanford. He would also like to thank Nicos Kapouleas for discussions which motivated him to consider this problem. The authors are also grateful to the anonymous referee for several remarks improving the exposition.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Stanford UniversityStanfordUSA
  2. 2.Brown UniversityProvidenceUSA

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