9 citations · 31 across the 29 of their papers we have counts for
13 papers · 1 filter
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…
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…
A study of measure-theoretic area formulas
Giacomo M. Leccese, Valentino Magnani
We present a complete study of measure-theoretic area formulas in metric spaces, providing different measurability conditions.
Characterizations of -rectifiability in homogenous groups
Kennedy Obinna Idu, Valentino Magnani, Francesco Paolo Maiale
A well known notion of -rectifiable set can be formulated in any metric space using Lipschitz images of subsets of . We prove some characterizations of -rectifi…