Lotay, JD;
Wei, Y;
(2017)
Laplacian flow for closed G2 structures: Shi-type estimates, uniqueness and compactness.
Geometric and Functional Analysis
, 27
(1)
pp. 165-233.
10.1007/s00039-017-0395-x.
Preview |
Text
art%3A10.1007%2Fs00039-017-0395-x.pdf Download (1MB) | Preview |
Abstract
We develop foundational theory for the Laplacian flow for closed G2 structures which will be essential for future study. (1). We prove Shi-type derivative estimates for the Riemann curvature tensor Rm and torsion tensor T along the flow, i.e. that a bound on Λ(x,t)=(|∇T(x,t)|2g(t)+|Rm(x,t)|2g(t))12 will imply bounds on all covariant derivatives of Rm and T. (2). We show that Λ(x,t) will blow up at a finite-time singularity, so the flow will exist as long as Λ(x,t) remains bounded. (3). We give a new proof of forward uniqueness and prove backward uniqueness of the flow, and give some applications. (4). We prove a compactness theorem for the flow and use it to strengthen our long time existence result from (2) to show that the flow will exist as long as the velocity of the flow remains bounded. (5). Finally, we study soliton solutions of the Laplacian flow.
| Type: | Article |
|---|---|
| Title: | Laplacian flow for closed G2 structures: Shi-type estimates, uniqueness and compactness |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00039-017-0395-x |
| Publisher version: | http://dx.doi.org/10.1007/s00039-017-0395-x |
| Language: | English |
| Additional information: | © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | Laplacian flow, G2 structure, Shi-type estimates, Uniqueness, Compactness, Soliton |
| UCL classification: | UCL 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/1534495 |
Archive Staff Only
 |
View Item |
