Date of Degree
PhD (Doctor of Philosophy)
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.
Copyright 2011 Mijia Lai
Lai, Mijia. "Fully nonlinear flows and Hessian equations on compact Kahler manifolds." doctoral dissertation, University of Iowa, 2011.