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.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/rka9-hb33 |
| Date | January 2023 |
| Creators | Smith, Kevin Jacob |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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