# Uniqueness of the Ricci flow on complete noncompact manifolds

@article{Chen2005UniquenessOT,
title={Uniqueness of the Ricci flow on complete noncompact manifolds},
author={Binglong Chen and Xiping Zhu},
journal={Journal of Differential Geometry},
year={2005},
volume={74},
pages={119-154}
}
• Published 21 May 2005
• Mathematics
• Journal of Differential Geometry
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…
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