You are here

Quantitative decompositions of Lipschitz mappings

Raanan Schul, Stony Brook University
Tuesday, January 26, 2021 - 1:30pm to 3:30pm
Zoom (link will be distributed via email; if you'd like to attend please email Silvia at

We discuss recent joint work with Guy C David. Any Lipschitz map from R^n can locally be approximated by a linear map. A 1988 theorem of Jones says that the domain can be broken up into a finite number of pieces, where the map is biLipschitz, except for a piece with small image content (in dimension n).  If the dimension of the image is smaller, then a 2012 theorem (joint with J. Azzam) shows that there is a large piece on which, after a global biLipschitz change of coordinates, the map behaves like a projection. With Guy C David, we recently improved upon this, getting that the domain may be broken up into pieces exhibiting this nice behavior, except for a piece with a `small’ image (in the appropriate sense).  All results above are quantitative! We will discuss the above results,  a construction by Kaufman showing it is sharp, and a very recent result showing this Kaufman construction is the only way to get such an example.

Event Type: 
Event Subcalendar: