Geometry of 1-codimensional measures in the Heisenberg groups
Andrea Merlo, SNS Pisa
Sala conferenze IMATI-CNR, Pavia – Martedì 17 Settembre 2019 h.15:00
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.