A Priori Estimates for the Homogeneous Monge-Ampère Equation on Kähler Manifolds Katherine Ann Brubaker 10.25394/PGS.9730208.v1 https://hammer.purdue.edu/articles/thesis/A_Priori_Estimates_for_the_Homogeneous_Monge-Amp_re_Equation_on_K_hler_Manifolds/9730208 <div>This thesis investigates the existence of smooth solutions to MA(<i>F</i>), proving a priori estimates on the leaves of the foliation that corresponds to smooth solutions. We demonstrate that sequences of leaves of Monge-Amp`ere foliations converge to holomorphic disks.</div> 2019-10-16 18:48:17 complex geometry several complex variables Non-linear partial differential equations foliation Kahler manifolds space of Kahler metrics Monge-Ampere equation Pure Mathematics not elsewhere classified Mathematical Sciences not elsewhere classified