DOI

10.17077/etd.3j5eth79

Document Type

Dissertation

Date of Degree

Spring 2011

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Fang, Hao

Second Advisor

Wang, Lihe

First Committee Member

Frohman, Charles

Second Committee Member

Seaman, Walter

Third Committee Member

Strohmer, Gerhard

Abstract

In this thesis, we will study a class of fully nonlinear flows on Kähler manifolds. This family of flows generalizes the previously studied J-flow. We use the quotients of elementary symmetric polynomials or log of them to construct the flow. We obtain a necessary and sufficient condition in terms of positivity of certain cohomology class to guarantee the convergence of the flow. The corresponding limit metric gives rise to a critical metric satisfying a Hessian type equation on the manifold. We shall also discuss several geometric applications of our main result.

Pages

v, 70 pages

Bibliography

Includes bibliographical references (pages 66-70).

Copyright

Copyright 2011 Mijia Lai

Included in

Mathematics Commons

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