Lecture Notes

Reimannian Geometry:
  The Gradient on Surfaces
  Worksheet on Abstract Manifolds
  Review Lecture(s)
  The Lie Bracket
  One-forms and Elementary Tensors
  Elementary Tensor Derivations
  Connections (Part I)
  Connections (Part II)
  Connections (Part III-draft)
  Curvature and General Tensors (Part I-draft)

Constant Mean Curvature Surfaces:
  Preliminaries (Draft)
  Introduction to Simple Bubbles (Draft)
  Area and Mean Curvature
  Some Basics of Linear Elliptic Equations
  The Equation of Constant Mean Curvature (Graphs Part I: Reduction to Leray-Schauder Fixed Point Theorem)
  The Equation of Constant Mean Curvature (Graphs Part II: Apriori Estimates)
  The Equation of Constant Mean Curvature (Parametric Solutions)
  Proofs of Maximum Principles and Reflection Techniques
  Proof of Leray-Schauder Fixed Point Theorem

Texts:

Riemannian Geometry by M.P. do Carmo

A Comprehensive Introduction to Differential Geometry Vol. I-V by M. Spivak

Curves and Surfaces by S. Montiel and A. Ros

Lecture Schedule and Homework