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

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 giv...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00039-017-0395-x

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Balliol College
Role:
Author
ORCID:
0000-0002-0456-4538
Publisher:
Springer Publisher's website
Journal:
Geometric and Functional Analysis Journal website
Volume:
27
Issue:
1
Pages:
165-233
Publication date:
2017-01-30
Acceptance date:
2016-12-30
DOI:
EISSN:
1420-8970
ISSN:
1016-443X
Source identifiers:
956120
Keywords:
Pubs id:
pubs:956120
UUID:
uuid:0c9426af-8297-4497-918f-9bad2374a705
Local pid:
pubs:956120
Deposit date:
2019-02-04

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