Geometric Measure Theory Reading Seminar

For students who have passed the real analysis qualifying exam and have taken some differential geometry (need to know differential forms):

I am running a Geometric Measure Theory study group using Morgan's book. We will meet Tuesdays 11:15-1:15 (4217).

We should get through Frank Morgan's book in the Spring, and then Ambrosio-Kirchheim's "Currents on Metric Spaces" and my new work with Stefan Wenger over the summer.

Students taking this as an independant study class will receive 5 pts per completed problem and will then be graded traditionally based upon their accumulated points (90 and up is an A etc).

Schedule:

• February 10: Hausdorff measures, Densities (Morgan 2.1-2.7)
• Feb 17: Review diffrential forms (meet without me)
• Feb 24: Conference at IAS worth attending
• Mar 3: Besicovitch Covering Theorem, Lebesgue and Hausdorff Measures (Morgan 2.7-2.10)
• Mar 10: Lipschitz Functions, Area and Coarea formulas (Morgan 3.1-3.9)
  submit Morgan problems 2.2, 2.4 on March 24
• Mar 24: Rectifiable Sets (Morgan 3.10-3.17)
  submit Morgan problems 3.4, 3.5, 3.6, 3.7, 3.8 on March 31
• Mar 31: Rectifiable Currents (Morgan 4.1-4.3)
  submit Morgan 4.6 and 4.7 on April 4
• April 4: Went over homework
  submit Morgan 4.16, 4.17, on April 21,
• April 21: Normal Currents and Flat Norm (Morgan 4.3-4.5)
  submit Morgan 4.10, 4.11, 4.12, 4.13, 4.14, 4.15 on April 28
• April 28: (posponed) Polyhedral Approximation (4.6) and Slicing (4.11) (Morgan 4.6-4.12)
  submit Morgan 4.18, 4.19, 4.20, 4.21 on May 19,
• May 5th: (posponed) Flat Compactness Theorem (Morgan Ch 5)
  submit Morgan 4.22, 5.2 on May 20