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<\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.
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This content will become publicly available on March 8, 2025
Eigenvalue lower bounds and splitting for modified Ricci flow
We prove sharp lower bounds for eigenvalues of the drift Laplacian for a modified Ricci flow. The modified Ricci flow is a system of coupled equations for a metric and weighted volume that plays an important role in Ricci flow. We will also show that there is a splitting theorem in the case of equality.
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- Award ID(s):
- 2304684
- NSF-PAR ID:
- 10531434
- Publisher / Repository:
- De Gruyter
- Date Published:
- Journal Name:
- Advanced Nonlinear Studies
- Volume:
- 24
- Issue:
- 1
- ISSN:
- 2169-0375
- Page Range / eLocation ID:
- 178 to 188
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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