Author : Xiangwen Zhang
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (841 download)
Book Synopsis Complex Monge-Ampère Equation and Its Applications in Complex Geometry by : Xiangwen Zhang
Download or read book Complex Monge-Ampère Equation and Its Applications in Complex Geometry written by Xiangwen Zhang and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The main threads of this thesis are related by the theme of the complex Monge-Ampère type equations. It consists of some analysis results from the partial differential equation aspect and several geometric consequences as applications.In the first part, we study the a priori estimates for complex Hessian type equations on Hermitian manifolds. These estimates are the key ingredients for the solvability of the corresponding equations by virtue of the continuity method. In particular, we establish the first and second order derivative estimates for complex Monge-Ampère equations which are analogous to Yau's estimates on Kãhler manifolds. In Chapter 3, we investigate the interior Schauder estimates of the solutions to complex Monge-Ampère equations. Moreover, aiming to extend such regularity results to more general geometric setting, we also establish the classical Bedford-Taylor's interior second order estimate and a local version of Calabi's third order ...