Topics in geometric analysis II

Topics in geometric analysis II

Every Tuesday,  10h30-12h00,  Room Ma10

Objectives 

To lay some foundations in modern geometric analysis.

 

Content

Geometric Analysis, which was traditionally dealing with smooth Riemannian manifolds has been developed over the last two decades to the context of non Riemannian metric spaces which may be quite irregular. This development has revitalized the subject of metric geometry which faded away after 1940. The goal of this course is to introduce the student to the basic notion of analysis on metric (measure) spaces, quasiconformal mappings, potential theory on metric spaces, etc. The subjects covered will vary each year.

 

Required prior knowledge

Basic culture in geometry, smooth manifolds, tensors, measure theory and functional analysis.
 

Schedule

In spring 2015, the course will take place on Monday morning, 10:3-12:00. Room MA 10 in the math. building at EPFL.
 

Subject for spring 2015

We will choose the subject according to the participants interests. We will start by studying some relation between geometry and potential theory.
 

Contact me for any question concerning this activity.

Marc Troyanov 

 
Tuesday February 24 :   Marc Troyanov    Capacity and distances in Lipshitz manifold.
I will discuss the problem of properly defining distances in a manifold having a Lipshitz metric. Following a suggestion of De Giorgi, De Cecco and Palmiari successfuly related this natural distance to some non linear capacities (Math. Z. 1991).
 
Tuesday March 3 :   Marc Troyanov    Cap Capacity and distances in Lipshitz manifold, continued.
 
Tuesday March 10 :   Adrien Marcone    The Cohn-Vossen inequality
The Cohn-Vossen inequality will be discussed. It states that the total curvature  of a complete Riemannian surface is at most 2pi times the Euler characteristic of the surface (for compact surfaces without boundary we have equality by Gauss-Bonnet).