Frank Liou
PHD Student
Department of Mathematics
University of California Davis


My Blog (In Chinese)
My Album

FrankMath World

TA Teaching 

2007 Fall Quarter/21B

2007 Winter Quarter/21C

2007 Spring Quarter/16B

Course that I've taken

1. 2007 Fall/Analysis/Math Fluid dynamics/Math Quantum mechanics
2. 2008 Winter/Analysis/Partial Differential Equations/Ordinary Differential Equations
3. 2008 Spring/Analysis/Partial Differential Equations/Differential Topology/Lie groups

Master Thesis

The Math Field That I am Interested with:

Lecture Notes

When I was a research asistant of National Center Theoretical Science in Taiwan, I gave a series of talks about the analysis on  Riemannian Manifolds.  What I focused on were spectral problems on Riemannian manifolds.  Before studying this topic, we need the gradient estimates, the Harnack inequality, of the Laplace equations on manifolds with possitive Ricci curvature.

The Harnack Inequality on manifolds with positive Ricci curvature

I have studied the inverse spectral theory for several years and also studied the infinite dimensional Hilbert manifolds related to the inverse spectral theory. The isospectral set of  the Schrodinger equation forms an infinite dimensional submanifold of the Hilbert space L^2[0,1]. We can construct the local chart to some l^2 space by using variational calculus. Here is one note about the basic idea of the construction of local chart.

The Inverse Dirichlet Problem


Some Useful Notel