Date of Degree
2011
Document Type
dissertation
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
Recommended Citation
Lai, Mijia. "Fully nonlinear flows and Hessian equations on compact Kahler manifolds." doctoral dissertation, University of Iowa, 2011.
http://ir.uiowa.edu/etd/1010.