Lecture notes on geometric analysis  Peter Li

  1. First and second variation formula for area
  2. Bishop comparison theorem
  3. Bochner-Weitzenbock formula
  4. Laplacian comparison theorem
  5. Poincare inequatility and the first eigenvalue
  6. Gradient esimate and Harnack inequality
  7. Mean value inequality
  8. Reilly formula and applications
  9. Isoperimetric inequalities and Sobolev inequality
  10. Lower bounds of isoperimetric inequlities
  11. Harnack inequality and regularity theory of De Giorgi-Nash-Moser