Pseudolocality for the Ricci Flow and Applications
By Albert Chau, Luen-Fai Tam, Chengjie Yu. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2007
79 citations recorded by the source corpus.
Abstract Perelman established a differential Li-Yau-Hamilton $\left( \text{LHY} \right)$ type inequality for fundamental solutions of the conjugate heat equation corresponding to the Ricci flow on compact manifolds. As an application of the $\text{LHY}$ inequality, Perelman proved a pseudolocality result for the Ricci flow on compact manifolds. In this article we provide the details for the proofs of these results in the case of a complete noncompact Riemannian manifold. Using these results we prove that under certain conditions, a finite time singularity of the Ricci flow must form within a compact set. The conditions are satisfied by asymptotically flatmanifolds. We also prove a long time existence result for the Kähler-Ricci flow on complete nonnegatively curved Kähler manifolds.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/08caa433d56f73b4178287403f6cf1d519c69d63
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Citations in the corpus
- Ricci flow on asymptotically Euclidean manifolds (2016, background): “Although in [16] they have only proved the case for the conjugate heat kernel, the same proof works for all f which satisfies [33, (3.”