Fall 2024
Xiaojun Huang
Course Description:
Introduction to Several Complex Variables and Subelliptic Analysis
1. Fourier Analysis and Soblev spaces theory
2. Pseudo-differential operators
3. H\"ormander's subelliptic estimates for sum of squares of a system of vector fields satisfying the finite type condition
4. Abstract CR structures
5. Boundary dbar operators and Kohn's microlocal analysis
6. Subelliptic multipliers and Hodge theory for compact strongly pseudoconvex CR manifolds
7. Boutet de Monvel theorem and Kohn-Rossi extension theorem
8. Harvey-Lawson theorem on solutions to Complex Plateau problems
Text:
We will follow an old Lecture Notes written by the Instructor.
Prerequisites:
One Complex Variable and Real Analysis. A little knowledge on Differential Manifold Theory will be helpful.
Schedule of Sections:
16:640:523 Schedule of Classes