Bounding sectional curvature along the Kähler-RICCI flow

Wei Dong Ruan; Yuguang Zhang; Zhenlei Zhang

doi:10.1142/S0219199709003673

Bounding sectional curvature along the Kähler-RICCI flow

Wei Dong Ruan^*
, Yuguang Zhang
, Zhenlei Zhang

^*Corresponding author for this work

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

7 Citations (Scopus)

Abstract

If a normalized KählerRicci flow g(t), t ∈ [0,∞), on a compact Kähler manifold M, dim M = n < 3, with positive first Chern class satisfies g(t) ∈ 2πc₁(M) and has curvature operator uniformly bounded in Lⁿ-norm, the curvature operator will also be uniformly bounded along the flow. Consequently, the flow will converge along a subsequence to a KählerRicci soliton.

Original language	English
Pages (from-to)	1067-1077
Number of pages	11
Journal	Communications in Contemporary Mathematics
Volume	11
Issue number	6
DOIs	https://doi.org/10.1142/S0219199709003673
Publication status	Published - Dec 2009
Externally published	Yes

Keywords

CheegerGromov convergence
Curvature operator
Gromov-Hausdorff convergence
Kähler-Einstein metric
Kähler-Ricci flow
Kähler-Ricci soliton

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title = "Bounding sectional curvature along the K{\"a}hler-RICCI flow",

abstract = "If a normalized K{\"a}hlerRicci flow g(t), t ∈ [0,∞), on a compact K{\"a}hler manifold M, dim M = n < 3, with positive first Chern class satisfies g(t) ∈ 2πc1(M) and has curvature operator uniformly bounded in Ln-norm, the curvature operator will also be uniformly bounded along the flow. Consequently, the flow will converge along a subsequence to a K{\"a}hlerRicci soliton.",

keywords = "CheegerGromov convergence, Curvature operator, Gromov-Hausdorff convergence, K{\"a}hler-Einstein metric, K{\"a}hler-Ricci flow, K{\"a}hler-Ricci soliton",

author = "Ruan, \{Wei Dong\} and Yuguang Zhang and Zhenlei Zhang",

year = "2009",

month = dec,

doi = "10.1142/S0219199709003673",

language = "English",

volume = "11",

pages = "1067--1077",

journal = "Communications in Contemporary Mathematics",

issn = "0219-1997",

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TY - JOUR

T1 - Bounding sectional curvature along the Kähler-RICCI flow

AU - Ruan, Wei Dong

AU - Zhang, Yuguang

AU - Zhang, Zhenlei

PY - 2009/12

Y1 - 2009/12

N2 - If a normalized KählerRicci flow g(t), t ∈ [0,∞), on a compact Kähler manifold M, dim M = n < 3, with positive first Chern class satisfies g(t) ∈ 2πc1(M) and has curvature operator uniformly bounded in Ln-norm, the curvature operator will also be uniformly bounded along the flow. Consequently, the flow will converge along a subsequence to a KählerRicci soliton.

AB - If a normalized KählerRicci flow g(t), t ∈ [0,∞), on a compact Kähler manifold M, dim M = n < 3, with positive first Chern class satisfies g(t) ∈ 2πc1(M) and has curvature operator uniformly bounded in Ln-norm, the curvature operator will also be uniformly bounded along the flow. Consequently, the flow will converge along a subsequence to a KählerRicci soliton.

KW - CheegerGromov convergence

KW - Curvature operator

KW - Gromov-Hausdorff convergence

KW - Kähler-Einstein metric

KW - Kähler-Ricci flow

KW - Kähler-Ricci soliton

UR - https://www.scopus.com/pages/publications/73949105198

U2 - 10.1142/S0219199709003673

DO - 10.1142/S0219199709003673

M3 - Article

AN - SCOPUS:73949105198

SN - 0219-1997

VL - 11

SP - 1067

EP - 1077

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - 6

ER -

Bounding sectional curvature along the Kähler-RICCI flow

Abstract

Keywords

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