Existence of Ricci flows of incomplete surfaces. (English) Zbl 1233.35123
Summary: 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.
MSC:
| 35K59 | Quasilinear parabolic equations |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |
| 58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
| 58J32 | Boundary value problems on manifolds |
| 30C80 | Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
instantaneous completeness; logarithmic fast diffusion equation; Schwarz-Pick-Ahlfors-Yau lemma; uniformization; maximal existence timeReferences:
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