Geometric Analysis Seminar
Fall 2012 - Fall 2014



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.


Fall 2014

September 19, X. Zhou:

A brief introduction to the viscosity solution

In this talk, we will give a brief introduction to viscosity solution theory. In particular, we will study the comparison principle for viscosity solutions to a general class of second-order fully nonlinear equations.


September 12, S. Malekzadeh:

A characterization of mappings of bounded length distortion


September 5, J. Mirra:

Brezis Nguyen Jacobian Determinant for W^((N-1)/N , N)


Fall 2013

November 4, S. Zimmerman:

Lipschitz Extensions Of Mappings Into Lipschitz-connected Metric Spaces


October 28, X. Zhou:

Sobolev Homeomorphism On A Sphere Containing An Arbitrary Cantor Set In The Image


October 21, S. Malekzadeh:

Metric Differentiability - Kirchheim, Rademacher Theorem


September 30, October 7, October 14, S. Zimmerman:

The unrectifiability of Hn


September 23, S. Malekzadeh:

Lusin condition (N) for W1,n functions - A new proof


September 16, J. Mirra:

Sphere Embeddings


Spring 2013

April 3, Qing Liu:

An elementary introduction to viscosity solution theory


March 27, S. Malekzadeh:

Measures on Rn and von Neumann theorem (II)


March 20, S. Malekzadeh:

Measures on Rn and von Neumann theorem (I)


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.


February 27, Dr. P. Hajlasz:

The theorem of Meyers and Ziemer


February 20, Soheil Malekzadeh:

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


February 6 - 8, Scott Sheffield:

PDEs, Politics and Tug-of-War


January 30, Kevin Wildrick:

The Heisenberg group as a metric space


January 23, S. Zimmerman:

Whitney Extension Theorem


January 9, J. Mirra:

Generalized Luzin's Theorem


Fall 2012

December 4, S. Malekzadeh:

Change of variables for locally Lipschitz mappings


November 28, X. Zhou:

The Hausdorff Dimension of the Cantor Set


November 14, P. Hajlasz:

Maximal functions and Sobolev spaces (Not yet available.)


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


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

The Brunn-Minkowski inequality.

The boxing inequality.


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