Degeneration of Kähler-Ricci solitons

Gang Tian; Zhenlei Zhang

doi:10.1093/imrn/rnr036

Degeneration of Kähler-Ricci solitons

Gang Tian, Zhenlei Zhang

Mathematics

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

14 Scopus citations

Abstract

Let (Y,d) be a Gromov-Hausdorff limit of n-dimensional closed shrinking Kähler-Ricci solitons with uniformly bounded volumes and Futaki invariants. We prove that off a closed subset of codimension at least 4, Y is a smooth manifold satisfying a shrinking Kähler-Ricci soliton equation. A similar convergence result for Kähler-Ricci flow of positive first Chern class is also obtained.

Original language	English (US)
Pages (from-to)	957-985
Number of pages	29
Journal	International Mathematics Research Notices
Volume	2012
Issue number	5
DOIs	https://doi.org/10.1093/imrn/rnr036
State	Published - Jan 1 2012

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnr036

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title = "Degeneration of K{\"a}hler-Ricci solitons",

abstract = "Let (Y,d) be a Gromov-Hausdorff limit of n-dimensional closed shrinking K{\"a}hler-Ricci solitons with uniformly bounded volumes and Futaki invariants. We prove that off a closed subset of codimension at least 4, Y is a smooth manifold satisfying a shrinking K{\"a}hler-Ricci soliton equation. A similar convergence result for K{\"a}hler-Ricci flow of positive first Chern class is also obtained.",

author = "Gang Tian and Zhenlei Zhang",

note = "Funding Information: This work was supported in part by National Science Foundation grants DMS-0847524 and DMS-0804095 (to G.T.) and by the National Science Foundation grant of China 09221010056 (to Z.Z.).",

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AU - Tian, Gang

AU - Zhang, Zhenlei

N1 - Funding Information: This work was supported in part by National Science Foundation grants DMS-0847524 and DMS-0804095 (to G.T.) and by the National Science Foundation grant of China 09221010056 (to Z.Z.).

PY - 2012/1/1

Y1 - 2012/1/1

N2 - Let (Y,d) be a Gromov-Hausdorff limit of n-dimensional closed shrinking Kähler-Ricci solitons with uniformly bounded volumes and Futaki invariants. We prove that off a closed subset of codimension at least 4, Y is a smooth manifold satisfying a shrinking Kähler-Ricci soliton equation. A similar convergence result for Kähler-Ricci flow of positive first Chern class is also obtained.

AB - Let (Y,d) be a Gromov-Hausdorff limit of n-dimensional closed shrinking Kähler-Ricci solitons with uniformly bounded volumes and Futaki invariants. We prove that off a closed subset of codimension at least 4, Y is a smooth manifold satisfying a shrinking Kähler-Ricci soliton equation. A similar convergence result for Kähler-Ricci flow of positive first Chern class is also obtained.

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DO - 10.1093/imrn/rnr036

M3 - Article

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VL - 2012

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EP - 985

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 5

ER -

Degeneration of Kähler-Ricci solitons

Abstract

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