Convergence of the Ricci flow toward a soliton

Natasa Sesum

doi:10.4310/CAG.2006.v14.n2.a4

Convergence of the Ricci flow toward a soliton

Natasa Sesum

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

24 Scopus citations

Abstract

We will consider a τ-flow, given by the equation d/dtg_ij = -2R_ij + 1/7tau;g_ij on a closed manifold M, for all times t ∈ [0, ∞). We will prove that if the curvature operator and the diameter of (M, g(t)) are uniformly bounded along the flow, then we have a sequential convergence of the flow toward the solitons. If we also assume that one of the limit solitons is integrable, then we have a convergence toward a unique soliton, up to a diffeomorphism.

Original language	English (US)
Pages (from-to)	283-343
Number of pages	61
Journal	Communications in Analysis and Geometry
Volume	14
Issue number	2
DOIs	https://doi.org/10.4310/CAG.2006.v14.n2.a4
State	Published - Mar 2006
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Geometry and Topology
Statistics, Probability and Uncertainty

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10.4310/CAG.2006.v14.n2.a4

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author = "Natasa Sesum",

year = "2006",

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doi = "10.4310/CAG.2006.v14.n2.a4",

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AB - We will consider a τ-flow, given by the equation d/dtgij = -2Rij + 1/7tau;gij on a closed manifold M, for all times t ∈ [0, ∞). We will prove that if the curvature operator and the diameter of (M, g(t)) are uniformly bounded along the flow, then we have a sequential convergence of the flow toward the solitons. If we also assume that one of the limit solitons is integrable, then we have a convergence toward a unique soliton, up to a diffeomorphism.

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JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

IS - 2

ER -

Convergence of the Ricci flow toward a soliton

Abstract

All Science Journal Classification (ASJC) codes

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