2018 Theses Doctoral

# The coupled Ricci flow and the anomaly flow over Riemann surface

In the first part of this thesis, we proved a pseudo-locality theorem for a coupled Ricci flow, extending Perelman’s work on Ricci flow to the Ricci flow coupled with heat equation. By use of the reduced distance and the pseudo-locality theorem, we showed that the parabolic rescaling of a Type I coupled Ricci flow with respect to a Type I singular point converges to a non-trivial Ricci soliton. In the second part of the thesis, we prove the existence of infinitely many solutions to the Hull- Strominger system on generalized Calabi-Gray manifolds, more specifically compact non-K \"ahler Calabi-Yau 3-folds with infinitely many distinct topological types and sets of Hodge numbers. We also studied the behavior of the anomaly flow on the generalized Calabi-Gray manifolds, and reduced it to a scalar flow on a Riemann surface. We obtained the long-time existence and convergence after rescaling in the case when the curvature of initial metric is small.

## Subjects

## Files

- Huang_columbia_0054D_14536.pdf application/pdf 516 KB Download File

## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- Phong, Duong H.
- Degree
- Ph.D., Columbia University
- Published Here
- April 13, 2018