Di Giovanni, Francesco;
(2021)
Convergence of Ricci flow solutions to Taub-NUT.
Communications in Partial Differential Equations
, 46
(8)
pp. 1521-1568.
10.1080/03605302.2021.1883651.
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Abstract
We study the Ricci flow starting at an SU(2) cohomogeneity-1 metric g0 on R4 with monotone warping coefficients and whose restriction to any hypersphere is a Berger metric. If g0 has bounded Hopf-fiber, curvature controlled by the size of the orbits and opens faster than a paraboloid in the directions orthogonal to the Hopf-fiber, then the flow converges to the Taub-NUT metric gTNUT in the Cheeger-Gromov sense in infinite time. We also classify the long-time behaviour when g0 is asymptotically flat. In order to identify infinite-time singularity models we obtain a uniqueness result for gTNUT.
| Type: | Article |
|---|---|
| Title: | Convergence of Ricci flow solutions to Taub-NUT |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1080/03605302.2021.1883651 |
| Publisher version: | https://doi.org/10.1080/03605302.2021.1883651 |
| Language: | English |
| Additional information: | Copyright © 2021 The Author(s). Published with license by Taylor and Francis Group, LLC This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10149046 |
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