SYLLABUS for Introduction to Geometric Analysis
TEXT: Introduciton to Geometric Analysis
INSTRUCTOR: C.J. Anna Sung
OFFICE: Math. Building 525 ; Tel: ext 62308; Email: cjsung@math.nthu.edu.tw
OFFICE HOURS: by appointment.
LECTURES: Friday 11:10-12:30 AM and 13:20-14:30
Contents
In this course, we will study Harmonic functions, Green's functions, and Spectral theorems on Riemannian Manifolds. We will build a connection between geometry and PDE at the graduate level.
(a) Gradient Estimate.
(b) Existence of Green's function.
(c) Harmonic function and end.
(d) Manifold with positive curvature.
(e) Manifold with positive bottom spectrum.
(f) Manifold with weigthed Poincar\'{e} inequality.
(g) Applications.

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.

REMARKS:
(1) Evaluation: Homework and Oral presentation(or Exam)(to be scheduled).
There is homework that must be handed in. The homework will be due in class on the designated day. You can discuss the homework with others in the class, but you must write up your homework solution by yourself. Thus, you should understand the solution and be able to reproduce it yourself.
(2) No late homework and make-up for exam.
(3) You have to show your work to receive any credit.
(4) Any student missing an exam without providing a legitimate excuse is given a grade of zero on that exam.
(5) Any student who wants to be excused from any of the scheduled exams must discuss the situation with me at least one week before the exam.
***'Turn off' the cellular phone in the class***

All the above information is subject to change, based on in-class announcement