LECTURES: Tuesday 10:10AM-11:25AM and Thursday 9:45-11:00AM.
課程說明(Course Description):
帶領學生研讀幾何分析的重要問題與其應用。
研讀相關論文,訓練學生思維能力
We study Harmonic functions, Green's functions and Spectrum theorems on
Riemannian
Manifolds.
References:
L. Evans: Partial Differential Equaitons
Jost: Riemannian Geometry and Geometric Analysis.
Davies and Safrov:Spectral Theory and Geometry.
Warner: Foundations of Differential Manifolds and Lie Groups.
Do Carmo: Riemannian Geometry.
P. Li: Lecture note on Geometric Analysis
R. Courant and D. Hilbert: Methods of Mathematical Physics. Vol. I and II.
E.B.Davies: Heat Kernels and spectral theory
Exam 50% + Homework 50%