As on arXiv
Abstract
In this paper, I computed the second variation formula of the generalized Einstein-Hilbert functional and prove that a Bismut-flat, Einstein manifold is linearly stable under some curvature assumption. In the last part of the paper, I prove that dynamical stability and linear stability are equivalent on a steady gradient generalized Ricci soliton which generalizes the result done by Kröncke, Haslhofer, Sesum, Raffero, and Vezzoni.
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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Dynamical stability of Pluriclosed and Generalized Ricci solitons
Topics Generalized & G₂ flows, Stability & uniqueness, Ricci solitons · Same author Kuan-Hui Lee · Shared terms “dynamical stability”, “generalized Einstein”, “Hilbert functional”
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Stability and moduli space of generalized Ricci solitons
Topics Generalized & G₂ flows, Stability & uniqueness, Ricci solitons · Same author Kuan-Hui Lee · Shared terms “Bismut flat”, “generalized Einstein”, “linearly stable”
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Linear stability of compact shrinking Ricci solitons
Topics Einstein metrics, Stability & uniqueness, Ricci solitons · Shared terms “linear stability”, “linearly stable”, “variation”
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The Cauchy problem for gradient generalized Ricci solitons on a bundle gerbe
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A -Hilbert functional in -geometry
Topics Generalized & G₂ flows · Shared terms “Hilbert functional”, “Einstein Hilbert”
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Generalized Ricci solitons and Einstein metrics on weak -contact manifolds
Topics Generalized & G₂ flows, Einstein metrics, Ricci solitons
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Homogeneous Generalized Ricci flows II
Topics Generalized & G₂ flows, Stability & uniqueness, Ricci solitons · Shared terms “Bismut flat”, “dynamical stability”
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Cylindrical generalized Ricci solitons in three dimensions
Topics Generalized & G₂ flows, Ricci solitons · Shared terms “gradient generalized”, “Raffero”, “steady gradient”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.