MATH6081 - Topics in Analysis I - 2022/23

General Information

Lecturer

• Jian-Ci Xiao
  • Office: LSB G07
  • Email:

Course Description

This is an introductory course to Geometric measure theory. Our specific topics will include:

- Covering theorems and differentiation of measures

- Hausdorff measures and dimension

- Weighted Hausdorff measures and Frostman's lemma

- Behaviors of sets under orthogonal projections

- Slicing measures and intersection with planes

- Energies and Fourier transform methods

- The distance set problem

- Rectifiability (if time permits)

Textbooks

• P. Mattila, Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability, Cambridge University Press, Cambridge, 1995.