Curvature tensor under the Ricci flow

By N. Šešum. 2003

126 citations recorded by the source corpus.

Consider the unnormalized Ricci flow (gjj)t = -2R ij for t ∈ [0, T), where T < oc. Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times t ∈ [0, T), then the solution can be extended beyond T. We prove that if the Ricci curvature is uniformly bounded under the flow for all times t ∈ [0, T), then the curvature tensor has to be uniformly bounded as well.

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

View Paper: https://www.semanticscholar.org/paper/b987f587e28da0495d1fddd9ba690e6c82b8beee

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

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Laplacian flow for closed G2 structures: Shi-type estimates, uniqueness and compactness (2015, methodology): “(Note that Sesum’s original proof [33] of the Ricci flow result used Perelman’s noncollapsing theorem, but Lei Ni pointed out that the result can be proved without the noncollapsing theorem.”
Regularity results for pluriclosed flow (2010, background): “Sesum for the Ricci flow ([23] Theorem 2), and already represents a significant improvement, as we have reduced the regularity requirement to understanding the Ricci-type curvature of a specific connection.”