Document Type

PhD diss.

Date of Degree

2011

Degree Name

PhD (Doctor of Philosophy)

Department

Mathematics

First Advisor

Hao Fang

Second Advisor

Lihe Wang

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

Bibliography

66-70

Copyright

Copyright 2011 Mijia Lai

Included in

Mathematics Commons

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