Degenerate Monge-Ampere equations over projective manifolds

• Main Author: Zhang, Zhou, Ph. D. Massachusetts Institute of Technology
• Other Authors: Gang Tian.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2006
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/1721.1/34685

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006. === This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. === Includes bibliographical references (p. 253-257). === In this thesis, we study degenerate Monge-Ampere equations over projective manifolds. The main degeneration is on the cohomology class which is Kähler in classic cases. Our main results concern the case when this class is semi-ample and big with certain generalization to more general cases. Two kinds of arguments are applied to study this problem. One is maximum principle type of argument. The other one makes use of pluripotential theory. So this article mainly consists of three parts. In the first two parts, we apply these two kinds of arguments separately and get some results. In the last part, we try to combine the results and arguments to achieve better understanding about interesting geometric objects. Some interesting problems are also mentioned in the last part for future consideration. The generalization of classic pluripotential theory in the second part may be of some interest by itself. === by Zhou Zhang. === Ph.D.