Speaker
Roberto Monti
(Università di Padova)
Description
In the Heisenberg group $H^1=\mathbb R^3$ we consider the
perimeter associated with a norm on the horizontal distribution.
The existence of isoperimetric sets is well-known. Assuming the $C^2_+$ regularity of the norm, we are able to classify isoperimetric sets of class $C^2$.
This is an extension to the Finsler case of a result by Ritorè and Rosales. Isoperimetric sets turn out to be foliated by geodesics for a natural optimal control problem. This property is consistent with Pansu's conjecture.
This is a joint work with Franceschi, Righini and Sigalotti.
