Geometric Analysis Seminar
Fall 2012 - Spring 2013



To the speakers:
Please write carefully notes from your talks. I will scan it and put on this webpage. The notes have to be written carefully with all details. It shoud be basically a verbarim copy of what you will present in class. The notes do not have to be written in TeX. Handwritten notes are OK provided they are legible.


October 10, P.Hajlasz: Sobolev inequality, isoperimetric inequality and Gromov's proof.

I covered the material from pages 166-193 from the following notes:

Sobolev spaces


October 17, P.Hajlasz: Brunn-Minkowski inequality, isoperimetric inequality and the boxing inequality.

The Brunn-Minkowski inequality.

The boxing inequality.


October 24, S.Zimmerman: The Sard theorem.

The talk is based on the proof that you can find in the following book on pages 195-198.

J.E.Marsden, T.Ratiu, R.Abraham, Manifolds, Tensor Analysis, and Applications

Sard's theorem


October 31, S. Malekzadeh: The change of variables formula under the miniman assumptions

The talk is based on the paper:

P.Hajlasz, Change of variables formula under minimal assumptions. Colloq. Math. 64 (1993), 93--101. pdf


November 14, P. Hajlasz:

Maximal functions and Sobolev spaces (Not yet available.)


November 28, X. Zhou:

The Hausdorff Dimension of the Cantor Set


December 4, S. Malekzadeh:

Change of variables for locally Lipschitz mappings


January 9, J. Mirra:

Generalized Luzin's Theorem


January 16, S. Zimmerman:

Whitney Extension Theorem


January 23, S. Zimmerman:

Whitney Extension Theorem


January 30, Kevin Wildrick:

The Heisenberg group as a metric space


February 6 - 8, Scott Sheffield:

PDEs, Politics and Tug-of-War


February 20, Soheil Malekzadeh:

Lusin's condition (N) and mappings of the class W^1,n


February 27, Dr. P. Hajlasz:

The theorem of Meyers and Ziemer


March 6, J. Mirra:

Classification of all Conformal Maps on domains in R^n (Assuming C^4 Differentiability)
This talk was based on pp. 255-283 of the notes.


March 20, S. Malekzadeh:

Measures on Rn and von Neumann theorem (I)


March 27, S. Malekzadeh:

Measures on Rn and von Neumann theorem (II)


April 3, Qing Liu:

An elementary introduction to viscosity solution theory