Degenerate Monge-Ampere equations over projective manifolds

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Zhang, Zhou, Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• Gang Tian.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/34685

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/34685