Open Access
September 2006 Uniqueness of the Ricci flow on complete noncompact manifolds
Bing-Long Chen, Xi-Ping Zhu
J. Differential Geom. 74(1): 119-154 (September 2006). DOI: 10.4310/jdg/1175266184


The Ricci flow is an evolution system on metrics. For a given metric as initial data, its local existence and uniqueness on compact manifolds were first established by Hamilton. Later on, De Turck gave a simplified proof. In the later part of 80’s, Shi 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. 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.


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Bing-Long Chen. Xi-Ping Zhu. "Uniqueness of the Ricci flow on complete noncompact manifolds." J. Differential Geom. 74 (1) 119 - 154, September 2006.


Published: September 2006
First available in Project Euclid: 30 March 2007

zbMATH: 1104.53032
MathSciNet: MR2260930
Digital Object Identifier: 10.4310/jdg/1175266184

Primary: 53C44

Rights: Copyright © 2006 Lehigh University

Vol.74 • No. 1 • September 2006
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