Stability of Ricci de Turck flow on Singular Spaces
arXiv:1802.02908 · doi:10.1007/s00526-019-1510-7
Abstract
In this paper we establish stability of the Ricci de Turck flow near Ricci-flat metrics with isolated conical singularities. More precisely, we construct a Ricci de Turck flow which starts sufficiently close to a Ricci-flat metric with isolated conical singularities and converges to a singular Ricci-flat metric under an assumption of integrability, linear and tangential stability. We provide a characterization of conical singularities satisfying tangential stability and discuss examples where the integrability condition is satisfied.
arXiv comment48 pages, published version
References in corpus (9)
- Kahler-Einstein metrics with edge singularities
- Existence of Ricci flows of incomplete surfaces
- Ricci flow on surfaces with conic singularities
- Smooth approximations of the Conical Kahler-Ricci flows
- Ricci flow of negatively curved incomplete surfaces
- Functional Determinants for Regular-Singular Laplace-type Operators
- Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone
- Stable and unstable Einstein warped products
- Local smoothing results for the Ricci flow in dimensions two and three