Uniqueness of Instantaneously Complete Ricci flows
نویسنده
چکیده
We prove uniqueness of instantaneously complete Ricci flows on surfaces. We do not require any bounds of any form on the curvature or its growth at infinity, nor on the metric or its growth (other than that implied by instantaneous completeness). Coupled with earlier work, particularly [25, 12], this completes the well-posedness theory for instantaneously complete Ricci flows on surfaces.
منابع مشابه
ricci flow of negatively curved incomplete surfaces
We show uniqueness of Ricci flows starting at a surface of uniformly negative curvature, with the assumption that the flows become complete instantaneously. Together with the more general existence result proved in [10], this settles the issue of well-posedness in this class.
متن کاملar X iv : 0 90 6 . 33 09 v 1 [ m at h . A P ] 1 8 Ju n 20 09 ricci flow of negatively curved incomplete surfaces
We show uniqueness of Ricci flows starting at a surface of uniformly negative curvature, with the assumption that the flows become complete instantaneously. Together with the more general existence result proved in [10], this settles the issue of well-posedness in this class.
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Given a completely arbitrary surface, whether or not it has bounded curvature, or even whether or not it is complete, there exists an instantaneously complete Ricci flow evolution of that surface that exists for a specific amount of time [GT11]. In the case that the underlying Riemann surface supports a hyperbolic metric, this Ricci flow always exists for all time and converges (after scaling b...
متن کاملExistence of Ricci flows of incomplete surfaces
We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.
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تاریخ انتشار 2013