Gianniotis, P;
Schulze, F;
(2018)
Ricci flow from spaces with isolated conical singularities.
Geometry & Topology
, 22
(7)
pp. 3925-3977.
10.2140/gt.2018.22.3925.
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Abstract
Let (M,g0) be a compact n–dimensional Riemannian manifold with a finite number of singular points, where the metric is asymptotic to a nonnegatively curved cone over (Sn−1,g). We show that there exists a smooth Ricci flow starting from such a metric with curvature decaying like C∕t. 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 (Sn−1/Γ,g), where Γ 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.
| Type: | Article |
|---|---|
| Title: | Ricci flow from spaces with isolated conical singularities |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.2140/gt.2018.22.3925 |
| Publisher version: | https://doi.org/10.2140/gt.2018.22.3925 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Ricci flow, singular initial data, conical singularities |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10051993 |
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