Kähler-Ricci solitons on compact complex manifolds with C 1(M) > 0

Huai Dong Cao; Gang Tian; Xiaohua Zhu

doi:10.1007/s00039-005-0522-y

Kähler-Ricci solitons on compact complex manifolds with C ₁(M) > 0

Huai Dong Cao, Gang Tian, Xiaohua Zhu

Mathematics

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

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.

Original language	English (US)
Pages (from-to)	697-719
Number of pages	23
Journal	Geometric and Functional Analysis
Volume	15
Issue number	3
DOIs	https://doi.org/10.1007/s00039-005-0522-y
State	Published - Jun 2005

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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10.1007/s00039-005-0522-y

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title = "K{\"a}hler-Ricci solitons on compact complex manifolds with C 1(M) > 0",

abstract = "In this paper, we discuss the relation between the existence of K{\"a}hler-Ricci solitons and a certain functional associated to some complex Monge-Amp{\`e}re 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 K{\"a}hler-Ricci soliton.",

author = "Cao, {Huai Dong} and Gang Tian and Xiaohua Zhu",

note = "Funding Information: G.T. partially supported by a NSF grant and the Simon fund. X.Z. partially supported by the NSFC Grant 10425102 and the Hou Y.D fund.",

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AU - Cao, Huai Dong

AU - Tian, Gang

AU - Zhu, Xiaohua

N1 - Funding Information: G.T. partially supported by a NSF grant and the Simon fund. X.Z. partially supported by the NSFC Grant 10425102 and the Hou Y.D fund.

PY - 2005/6

Y1 - 2005/6

N2 - 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.

AB - 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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JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 3

ER -

Kähler-Ricci solitons on compact complex manifolds with C ₁(M) > 0

Abstract

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