Communications in Analysis and Geometry
Volume 26 (2018)
Pseudo-locality for a coupled Ricci flow
Pages: 585 – 626
Let $(M, g, \phi)$ be a solution to the Ricci flow coupled with the heat equation for a scalar field $\phi$. We show that a complete, $\kappa$-noncollapsed solution $(M, g, \phi)$ to this coupled Ricci flow with a Type I singularity at time $T \lt \infty$ will converge to a non-trivial Ricci soliton after parabolic rescaling, if the base point is Type I singular. A key ingredient is a version of Perelman pseudo-locality for the coupled Ricci flow.
2010 Mathematics Subject Classification
This work was supported in part by NSF grant DMS-12-66033.
Received 3 April 2016
Published 27 July 2018