Tuesday, 17 September 2019, 3 p.m. (sharp),

Andrea Merlo, SNS Pisa,

at the conference room of IMATI CNR in Pavia, will give a lecture titled:

Geometry of 1-codimensional measures in the Heisenberg groups

At the end a refreshment will be organized.


Abstract. Characterisation of rectifiable measures in Euclidean spaces
through the existence of the density has been a longstanding problem
for Geometric Measure Theory until the complete answer by D. Preiss in
1987. The question of how in more general metric spaces existence of
density can affect any kind of gain in terms of regularity of the
measure is a completely open problem. In this talk I will discuss how
the mere existence of the 1-codimensional density for a measure in the
Heisenberg groups endowed with the Koranyi metric implies that almost
everywhere the tangents to the measure are flat.