Theses Doctoral

C² estimates in non-Kähler geometry

Smith, Kevin Jacob

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.


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More About This Work

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