Linear and dynamical stability of Ricci-flat metrics

By N. Šešum. 2004

92 citations recorded by the source corpus.

We can talk about two kinds of stability of the Ricci flow at Ricci flat metrics. One of them is a linear stability, defined with respect to Perelman's functional $\mathcal{F}$. The other one is a dynamical stability and it refers to a convergence of a Ricci flow starting at any metric in a neighbourhood of a considered Ricci flat metric. We show that dynamical stability implies linear stability. We also show that a linear stability together with the integrability assumption imply dynamical stability. As a corollary we get a stability result for $K3$ surfaces part of which has been done in \cite{dan2002}.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fe6ee5dbf1d445765af3d37b65b87e2f462bc4ee

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Robert Haslhofer
2. Reto Müller
3. Reto Muller
4. Ovidiu Munteanu
5. Jiaping Wang
6. G. Huisken
7. Bruce Kleiner
8. Richard Bamler

In Astronomy and Astrophysics

1. Robert Haslhofer
2. Reto Müller
3. Reto Muller
4. Jiaping Wang
5. Ovidiu Munteanu

In Geometry and Topology

1. Robert Haslhofer
2. Reto Müller
3. Ovidiu Munteanu
4. Jiaping Wang
5. G. Huisken
6. Bruce Kleiner
7. Richard Bamler

Citations in the corpus

• Stability of Euclidean space under Ricci flow (2007, unknown): “Šešum [4, 15].”
• Dynamical stability and instability of Ricci-flat metrics (2013, background): “In the present article, we prove that it is indeed possible to completely remove this integrability assumption imposed by Sesum and Haslhofer, i.e. we prove the following.”