Linear stability of algebraic Ricci solitons
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Michael Jablonski
,
Peter Petersen
Abstract
We consider a modified Ricci flow equation whose stationary solutions include Einstein and Ricci soliton metrics, and we study the linear stability of those solutions relative to the flow. After deriving various criteria that imply linear stability, we turn our attention to left-invariant soliton metrics on (non-compact) simply connected solvable Lie groups and prove linear stability of many such metrics. These include an open set of two-step solvsolitons, all two-step nilsolitons, two infinite families of three-step solvable Einstein metrics, all nilsolitons of dimensions six or less, and all solvable Einstein metrics of dimension seven or less with codimension-one nilradical. For each linearly stable metric, dynamical stability follows from a generalization of the techniques of Guenther, Isenberg, and Knopf.
Funding source: NSF
Award Identifier / Grant number: DMS-1105647
Funding source: NSF
Award Identifier / Grant number: DMS-1006677
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Congruence kernels around affine curves
- On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties
- On the splitting of quasilinear p-forms
- Graded quiver varieties and derived categories
- On the limit of spectral measures associated to a test configuration of a polarized Kähler manifold
- Static Klein–Gordon–Maxwell–Proca systems in 4-dimensional closed manifolds. II
- Linear stability of algebraic Ricci solitons
- Dynamical stability of algebraic Ricci solitons
- Erratum to Dynamics of the Krichever construction in several variables (J. reine angew. Math. 572 (2004), 111–138)
- Addendum: The case of closed surfaces (Boundary value problems on planar graphs and flat surfaces with integer cone singularities I: The Dirichlet problem)
Articles in the same Issue
- Frontmatter
- Congruence kernels around affine curves
- On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties
- On the splitting of quasilinear p-forms
- Graded quiver varieties and derived categories
- On the limit of spectral measures associated to a test configuration of a polarized Kähler manifold
- Static Klein–Gordon–Maxwell–Proca systems in 4-dimensional closed manifolds. II
- Linear stability of algebraic Ricci solitons
- Dynamical stability of algebraic Ricci solitons
- Erratum to Dynamics of the Krichever construction in several variables (J. reine angew. Math. 572 (2004), 111–138)
- Addendum: The case of closed surfaces (Boundary value problems on planar graphs and flat surfaces with integer cone singularities I: The Dirichlet problem)
