9 citations · 31 across the 29 of their papers we have counts for
39 papers
Stokes' theorem on positively graded groups
Valentino Magnani, Francesca Tripaldi
This paper studies the validity of Stokes' theorem for differential subcomplexes naturally adapted to the noncommutative geometry of positively graded Lie groups, with particular e…
A minimal regularity for the area formula in the Engel group
Francesca Corni, Fares Essebei, Valentino Magnani
We prove that the upper blow-up theorem in the Engel group holds for submanifolds. Combining this result with the known negligibility of the singular set, we obtain an integr…
Symmetry results for the area formula in homogeneous groups
Francesca Corni, Valentino Magnani
We prove that if the shape of the metric unit ball in a homogeneous group enjoys a precise symmetry property, then the associated distance yields the standard form of the area form…
The Michor-Mumford conjecture in Hilbertian H-type groups
Valentino Magnani, Daniele Tiberio
We introduce infinite dimensional Hilbertian H-type groups equipped with weak, graded, left invariant Riemannian metrics. For these Lie groups, we show that the vanishing of the ge…
Area of intrinsic graphs in homogeneous groups
Francesca Corni, Valentino Magnani
We establish an area formula for the spherical measure of intrinsic graphs of any codimension in homogeneous groups. Our approach relies on the assumption that the map defining the…
Surface measure on, and the local geometry of, sub-Riemannian manifolds
Sebastiano Don, Valentino Magnani
We prove an integral formula for the spherical measure of hypersurfaces in equiregular sub-Riemannian manifolds. Among various technical tools, we establish a general criterion for…