A Compactness Property for Solutions of the Ricci Flow

@article{Hamilton1995ACP,
  title={A Compactness Property for Solutions of the Ricci Flow},
  author={Richard S. Hamilton},
  journal={American Journal of Mathematics},
  year={1995},
  volume={117},
  pages={545}
}
  • R. Hamilton
  • Published 1 June 1995
  • Mathematics
  • American Journal of Mathematics
View via Publisher
343 Citations
Highly Influential Citations
29
Background Citations
55
Methods Citations
47
Results Citations
7

343 Citations

Citation Type

Citation Type

Convergence of Hermitian manifolds and the Type IIB flow
The Type IIB flow is a flow of conformally balanced complex manifolds introduced by Phong, Picard, and Zhang, about whose singularities little is as yet known. We formulate convergence criteria for…
Cheeger-Gromov compactness for manifolds with boundary
We prove Cheeger-Gromov convergence for a subsequence of a given sequence of manifolds (with boundary) of bounded geometry.
Uniqueness of Ricci Flow Solution on Non-compact Manifolds and Integral Scalar Curvature Bound
of the Dissertation Uniqueness of Ricci Flow Solution on Non-compact Manifolds and Integral Scalar Curvature Bound
A note on singular time of mean curvature flow
We show that mean curvature flow of a compact submanifold in a complete Riemannian manifold cannot form singularity at time infinity if the ambient Riemannian manifold has bounded geometry and…
Expanding solitons with non-negative curvature operator coming out of cones
We consider Ricci flow of complete Riemannian manifolds which have bounded non-negative curvature operator, non-zero asymptotic volume ratio and no boundary. We prove scale invariant estimates for…
Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics
By exploiting Perelman's pseudolocality theorem, we prove a new compactness theorem for Ricci flows. By optimising the theory in the two-dimensional case, and invoking the theory of quasiconformal…
Generalized Ricci flow I: Higher derivatives estimates for compact manifolds
We consider a generalized Ricci flow with a given (not necessarily closed) three-form and establish the higher derivatives estimates for compact manifolds. As an application, we prove the compactness…
On long-time existence for the flow of static metrics with rotational symmetry
B List has proposed a geometric flow whose fixed points correspond to solutions of the static Einstein equations of general relativity. This flow is now known to be a certain Hamilton-DeTurck flow…
On the simply connectedness of non-negatively curved K\
We study complete noncompact long time solutions $(M, g(t))$ to the K\"ahler-Ricci flow with uniformly bounded nonnegative holomorphic bisectional curvature. We will show that when the Ricci…
The Calabi flow on toric Fano surface
We prove the longtime existence and convergence of the Calabi flow on toric Fano surfaces in a large family of Kahler classes where the class has positive extremal Hamiltonian potential and the…
...
1
2
3
4
5
...