A Priori Estimates of the Degenerate Monge-Ampère Equation on Compact Kähler Manifolds

Download or read book A Priori Estimates of the Degenerate Monge-Ampère Equation on Compact Kähler Manifolds written by Sebastien Picard and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "The regularity theory of the degenerate complex Monge-Ampère equation is studied. First, the equation is considered on a compact Kahler manifold without boundary. Accordingly, some background information on Kahler geometry is presented. Given a solution of the degenerate complex Monge-Ampère equation, it is shown that its oscillation and gradient can be bounded. The Laplacian of the solution is also estimated. There is a slight improvement from the literature on the conditions required in order to obtain the estimate on the Laplacian of the solution, however the estimates developed only hold in the case of manifolds with non-negative bisectional curvature. As an application, a Dirichlet problem in complex space is considered. The obtained estimates are used to show existence and uniqueness of pluri-subharmonic solutions to the degenerate complex Monge-Ampere equation in a domain in complex space." --