Math 597, Topics in Math I Fall 2015

Course Information

  • Title: Introduction to non-smooth analysis and geometry.
  • Course Meetings MWF 10:00-10:50 am in 2-105 Wilson Hall.
  • Office hours: By appointment.

Lecture Notes

  • Set 1 Introduction and motivation
  • Set 2 Metric measure spaces
  • Set 3 Covering theorems
  • Set 4 Lebesgue's Differentiation Theorem
  • Set 5 Functions of bounded variation and absolute continuity.
  • Set 6 Rademacher's Theorem
  • Set 7 The local Lipschitz constant and Stepanov's Theorem
  • Set 8 An introduction to Cheeger's measurable differentiable structures
  • Set 9 Upper gradients
  • Set 10 The PoincarĂ© inequality in Euclidean space
  • Set 11 Examples of PoincarĂ© inequality spaces
  • Set 12 An introduction to the sub-Riemannian Heisenberg group
  • Set 13 Gromov-Hausdorff Convergence
  • Set 14 The Lip-lip condition
  • Set 15 The Lip-lip condition and finite dimensionalit