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Kähler–Ricci solitons on compact complex manifolds with C1(M) > 0

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Geometric & Functional Analysis GAFA Aims and scope Submit manuscript

Abstract.

In this paper, we discuss the relation between the existence of Kähler–Ricci solitons and a certain functional associated to some complex Monge–Ampère equation on compact complex manifolds with positive first Chern class. In particular, we obtain a strong inequality of Moser–Trudinger type on a compact complex manifold admitting a Kähler–Ricci soliton.

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Author notes

  1. Gang Tian

    Present address: Department of Mathematics,  , Princeton, NJ, 08544-1000, USA

Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, 77843, USA

    Huai-Dong Cao

  2. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Gang Tian

  3. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Gang Tian

  4. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Xiaohua Zhu

Authors
  1. Huai-Dong Cao
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  2. Gang Tian
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  3. Xiaohua Zhu
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Corresponding author

Correspondence to Huai-Dong Cao.

Additional information

Received: October 2004 Revised: February 2005 Accepted: February 2005

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Cao, HD., Tian, G. & Zhu, X. Kähler–Ricci solitons on compact complex manifolds with C1(M) > 0. GAFA, Geom. funct. anal. 15, 697–719 (2005). https://doi.org/10.1007/s00039-005-0522-y

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  • DOI: https://doi.org/10.1007/s00039-005-0522-y

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