2023 Theses Doctoral

# C² estimates in non-Kähler geometry

We study Monge-Ampère-type equations on compact complex manifolds. We prove a C² estimate for solutions to a general class of non-concave parabolic equations, extending work from the Kähler setting. Next we prove C⁰, C², and curvature estimates for solutions to a particular continuity path of elliptic equations on specific examples of non-Kähler manifolds, adapting work on the Chern-Ricci flow.

In each case the estimates give a certain type of convergence of the solutions. The estimates are obtained by maximum principle arguments, and in the first part of this work we set up a general framework that facilitates the various C² estimates which follow.

## Subjects

## Files

- Smith_columbia_0054D_17749.pdf application/pdf 337 KB Download File

## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- Phong, Duong Hong
- Degree
- Ph.D., Columbia University
- Published Here
- April 19, 2023