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Ricci flow from spaces
with isolated conical singularities
Panagiotis Gianniotis and Felix Schulze |
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Geometry & Topology 22 (2018) 3925–3977
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Abstract |
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Let be a compact –dimensional Riemannian manifold with a finite number of singular points, where the metric is asymptotic to a nonnegatively curved cone over . We show that there exists a smooth Ricci flow starting from such a metric with curvature decaying like . The initial metric is attained in Gromov–Hausdorff distance and smoothly away from the singular points. In the case that the initial manifold has isolated singularities asymptotic to a nonnegatively curved cone over , where acts freely and properly discontinuously, we extend the above result by showing that starting from such an initial condition there exists a smooth Ricci flow with isolated orbifold singularities. |
Keywords
Ricci flow, singular initial data, conical singularities
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Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 58J47
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References |
Publication
Received: 9 January 2017
Revised: 21 February 2018
Accepted: 1 July 2018
Published: 6 December 2018
Proposed: Bruce Kleiner
Seconded: Gang Tian, John Lott
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Authors |
| Panagiotis Gianniotis | |
| Department of Mathematics University of Toronto Toronto, ON Canada |
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| Felix Schulze | |
| Department of Mathematics University College London London United Kingdom |
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