A gradient flow of isometric $G_2$ structures

  title={A gradient flow of isometric \$G\_2\$ structures},
  author={Shubham Dwivedi and Panagiotis Gianniotis and Spiro Karigiannis},
We study a flow of G2-structures that all induce the same Riemannian metric. This isometric flow is the negative gradient flow of an energy functional. We prove Shi-type estimates for the torsion tensor T along the flow. We show that at a finite-time singularity the torsion must blow up, so the flow will exist as long as the torsion remains bounded. We prove a Cheeger–Gromov type compactness theorem for the flow. We describe an Uhlenbeck-type trick which together with a modification of the… Expand
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