Degenerate Monge-Ampere equations over projective manifolds
Name
71316778-MIT.pdf
Description
Full printable version
Size
1.11 MB
Format
Adobe PDF
Checksum (MD5)
678990885c21269d25f07cc6c353355e
Author(s)
Zhang, Zhou, Ph. D. Massachusetts Institute of Technology
Advisor(s)
Gang Tian.
Date Issued
2006
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
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).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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