Laplacian flow for closed G2 structures: Shi-type estimates, uniqueness and compactness

Jason D. Lotay University of Oxford Yong Wei Australian National University

Differential Geometry mathscidoc:1908.10007

Geometric and Functional Analysis, 27, (1), 165-233, 2017.2
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))^{1/2} 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.
No keywords uploaded!
[ Download ] [ 2019-08-19 18:16:43 uploaded by WeiYong ] [ 679 downloads ] [ 0 comments ]
@inproceedings{jason2017laplacian,
  title={Laplacian flow for closed G2 structures: Shi-type estimates, uniqueness and compactness},
  author={Jason D. Lotay, and Yong Wei},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190819181644097810414},
  booktitle={Geometric and Functional Analysis},
  volume={27},
  number={1},
  pages={165-233},
  year={2017},
}
Jason D. Lotay, and Yong Wei. Laplacian flow for closed G2 structures: Shi-type estimates, uniqueness and compactness. 2017. Vol. 27. In Geometric and Functional Analysis. pp.165-233. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190819181644097810414.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved