Uniqueness of the Ricci Flow on Complete Noncompact Manifolds
Abstract
The Ricci flow is an evolution system on metrics. For a given metric as initial data, its local existence and uniqueness on compact manifolds was first established by Hamilton \cite{Ha1}. Later on, De Turck \cite{De} gave a simplified proof. In the later of 80's, Shi \cite{Sh1} generalized the local existence result to complete noncompact manifolds. However, the uniqueness of the solutions to the Ricci flow on complete noncompact manifolds is still an open question. Recently it was found that the uniqueness of the Ricci flow on complete noncompact manifolds is important in the theory of the Ricci flow with surgery. In this paper, we give an affirmative answer for the uniqueness question. More precisely, we prove that the solution of the Ricci flow with bounded curvature on a complete noncompact manifold is unique.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2005
 DOI:
 10.48550/arXiv.math/0505447
 arXiv:
 arXiv:math/0505447
 Bibcode:
 2005math......5447C
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Analysis of PDEs
 EPrint:
 33 pages (Previous version has some typing errors, the present one is correct.)