%0 Thesis %A Brubaker, Katherine Ann %D 2019 %T A Priori Estimates for the Homogeneous Monge-Ampère Equation on Kähler Manifolds %U https://hammer.purdue.edu/articles/thesis/A_Priori_Estimates_for_the_Homogeneous_Monge-Amp_re_Equation_on_K_hler_Manifolds/9730208 %R 10.25394/PGS.9730208.v1 %2 https://hammer.purdue.edu/ndownloader/files/17435933 %K complex geometry %K several complex variables %K Non-linear partial differential equations %K foliation %K Kahler manifolds %K space of Kahler metrics %K Monge-Ampere equation %K Pure Mathematics not elsewhere classified %K Mathematical Sciences not elsewhere classified %X
This thesis investigates the existence of smooth solutions to MA(F), 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.
%I Purdue University Graduate School