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Existence of Ricci Flows of Incomplete Surfaces |
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| Authors: | Gregor Giesen Peter M Topping |
| Institution: | 1. Department of Mathematics , University of Warwick , Coventry, England g.giesen@warwick.ac.uk;3. Department of Mathematics , University of Warwick , Coventry, England |
| Abstract: | 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. |
| Keywords: | Instantaneous completeness Logarithmic fast diffusion equation Ricci flow Schwarz-Pick-Ahlfors-Yau lemma Uniformization |