Optimal Curvature Estimates for Homogeneous Ricci Flows

DOI10.1093/imrn/rnx256zbMath1457.53075arXiv1604.02625OpenAlexW2963591274MaRDI QIDQ5855166

Christoph Böhm, Ramiro A. Lafuente, Miles Simon

Publication date: 15 March 2021

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.02625

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Ricci flows (53E20)

Related Items (13)

On the long-time behavior of immortal Ricci flows ⋮ Immortal homogeneous Ricci flows ⋮ A compactness theorem for locally homogeneous spaces ⋮ Ancient solutions of the Ricci flow on bundles ⋮ Convergence of locally homogeneous spaces ⋮ Collapsed ancient solutions of the Ricci flow on compact homogeneous spaces ⋮ Kähler-Ricci flow on rational homogeneous varieties ⋮ A local version of the Myers–Steenrod theorem ⋮ Diverging sequences of unit volume invariant metrics with bounded curvature ⋮ On the stable set of an analytic gradient flow ⋮ The projected homogeneous Ricci flow and its collapses with an application to flag manifolds ⋮ Ancient solutions of the homogeneous Ricci flow on flag manifolds ⋮ On the Ricci flow of homogeneous metrics on spheres

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Scalar curvature behavior of homogeneous Ricci flows
• The evolution of positively curved invariant Riemannian metrics on the Wallach spaces under the Ricci flow
• The Ricci flow in a class of solvmanifolds
• The Ricci flow for simply connected nilmanifolds
• On type-I singularities in Ricci flow
• The Ricci flow approach to homogeneous Einstein metrics on flag manifolds
• Ricci flow on three-dimensional, unimodular metric Lie algebras
• The conjugate heat equation and ancient solutions of the Ricci flow
• On trajectories of analytic gradient vector fields
• Geometric estimates for the logarithmic fast diffusion equation
• On local and global existence of Killing vector-fields
• Backward Ricci flow on locally homogeneous 3-manifolds
• Ricci flow on locally homogeneous closed 4-manifolds
• On the long time behavior of homogeneous Ricci flows
• Convergence and rigidity of manifolds under Ricci curvature bounds
• The existence of type II singularities for the Ricci flow on \(S^{n+1}\)
• The geometry of compact homogeneous spaces with two isotropy summands
• The Ricci flow for nilmanifolds
• Dimensional reduction and the long-time behavior of Ricci flow
• Existence and non-existence of homogeneous Einstein metrics
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Counter-example to the second Singer's theorem
• \(C^ \alpha\)-compactness for manifolds with Ricci curvature and injectivity radius bounded below
• Ricci flow of locally homogeneous geometries on closed manifolds
• Inhomogeneous Einstein metrics on low-dimensional spheres and other low-dimensional spaces
• A remark on locally homogeneous Riemannian spaces
• Invariant Einstein metrics on certain homogeneous spaces
• High Singer invariant and equality of curvature
• Immortal homogeneous Ricci flows
• A variational approach for compact homogeneous Einstein manifolds
• Three-manifolds with positive Ricci curvature
• Quasi-convergence of model geometries under the Ricci flow
• Ricci flow of homogeneous manifolds
• Ricci flow on homogeneous spaces with two isotropy summands
• Nonnegatively curved manifolds with finite fundamental groups admit metrics with positive Ricci curvature
• On the long-time behavior of type-III Ricci flow solutions
• Homogeneous Einstein metrics and simplicial complexes
• The existence of invariant Einstein metrics on a compact homogeneous space
• Backwards Uniqueness for the Ricci Flow
• Two remarks on the length spectrum of a Riemannian manifold
• Ancient solutions of Ricci flow on spheres and generalized Hopf fibrations
• Noncompact shrinking four solitons with nonnegative curvature
• On gradient Ricci solitons with symmetry
• On normal homogeneous Einstein manifolds
• Sur la courbure des métriques riemanniennes invariantes des groupes de Lie et des espaces homogènes
• On the Upper Estimate of the Heat Kernel of a Complete Riemannian Manifold
• An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures
• Self-similar behaviour for the equation of fast nonlinear diffusion
• Riemannian Geometry

This page was built for publication: Optimal Curvature Estimates for Homogeneous Ricci Flows