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Ricci flow from spaces with isolated conical singularities
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Gianniotis, Panagiotis and Schulze, Felix (2018) Ricci flow from spaces with isolated conical singularities. Geometry & Topology, 22 (7). pp. 3925-3977. doi:10.2140/gt.2018.22.3925 ISSN 1364-0380.
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Official URL: http://dx.doi.org/10.2140/gt.2018.22.3925
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 negatively 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.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Geometry & Topology | ||||||||
Publisher: | Geometry & Topology Publications | ||||||||
ISSN: | 1364-0380 | ||||||||
Official Date: | 6 December 2018 | ||||||||
Dates: |
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Volume: | 22 | ||||||||
Number: | 7 | ||||||||
Page Range: | pp. 3925-3977 | ||||||||
DOI: | 10.2140/gt.2018.22.3925 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access |
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