Seminar

Differentiability of Lipschitz functions and tangents of sets

We will show how elementary product decompositions of measures can detect directionality in sets, and show how this can be used to describe non-differentiability sets of Lipschitz functions on R^n, and to understand the phenomena that occur because of behaviour of Lipschitz functions around the points of null sets.

In order to prove this we will need to prove results about the geometry of sets of small Lebesgue measure: we show that sets of small measure are always contained in a "small" collection of Lipschitz surfaces.

The talk is based on a joint work
with G. Alberti, P. Jones and D. Preiss.