13 citations · 63 across the 19 of their papers we have counts for
22 papers
Plateau's Problem for intrinsic graphs in the Heisenberg Group
Roberto Monti, Giacomo Vianello
Using a geometric construction, we solve Plateau's Problem in the Heisenberg group for intrinsic graphs defined on a convex domain , under a smallness condition…
Not all sub-Riemannian minimizing geodesics are smooth
Yacine Chitour, Frédéric Jean, Roberto Monti +4
A longstanding open question in sub-Riemannian geometry is the following: are sub-Riemannian length minimizers smooth? We give a negative answer to this question, exhibiting an exa…
Mean value formulas on surfaces in Grushin spaces
Valentina Franceschi, Roberto Monti, Alessandro Socionovo
We prove (sub)mean value formulas at the point for (sub)harmonic functions a on a hypersurface where the differentiable structure and the surface…
Higher order Goh conditions for singular extremals of corank 1
Francesco Boarotto, Roberto Monti, Alessandro Socionovo
We prove Goh conditions of order n for strictly singular length minimizing curves of corank 1, under the assumption that the lower order intrinsic differentials of the end-point ma…
Nonminimality of spirals in sub-Riemannian manifolds
Roberto Monti, Alessandro Socionovo
We show that in analytic sub-Riemannian manifolds of rank 2 satisfying a commutativity condition spiral-like curves are not length minimizing near the center of the spiral. The pro…
The isoperimetric problem for regular and crystalline norms in
Valentina Franceschi, Roberto Monti, Alberto Righini +1
We study the isoperimetric problem for anisotropic left-invariant perimeter measures on , endowed with the Heisenberg group structure. The perimeter is associated with…
Third order open mapping theorems and applications to the end-point map
Francesco Boarotto, Roberto Monti, Francesco Palmurella
This paper is devoted to a third order study of the end-point map in sub-Riemannian geometry. We first prove third order open mapping results for maps from a Banach space into a fi…
A Trace theorem for Martinet--type vector fields
Daniele Gerosa, Roberto Monti, Daniele Morbidelli
In we consider the vector fields \[ X_1 =\frac{ \partial }{\partial x},\qquad X_2 =\frac{ \partial }{\partial y}+ |x|^α\frac{ \partial }{\partial z}, \] where $α\in\…
John and uniform domains in generalized Siegel boundaries
Roberto Monti, Daniele Morbidelli
Given the pair of vector fields and where , we gi…
On tangent cones to length minimizers in Carnot-Carathéodory spaces
Roberto Monti, Alessandro Pigati, Davide Vittone
We give a detailed proof of some facts about the blow-up of horizontal curves in Carnot-Carathéodory spaces.
Improved Lipschitz approximation of -perimeter minimizing boundaries
Roberto Monti, Giorgio Stefani
We prove two new approximation results of -perimeter minimizing boundaries by means of intrinsic Lipschitz functions in the setting of the Heisenberg group with $…
CMC spheres in the Heisenberg group
Valentina Franceschi, Francescopaolo Montefalcone, Roberto Monti
We study a family of spheres with constant mean curvature (CMC) in the Riemannian Heisenberg group . These spheres are conjectured to be the isoperimetric sets of . We pr…
Existence of tangent lines to Carnot-Carathéodory geodesics
Roberto Monti, Alessandro Pigati, Davide Vittone
We show that length minimizing curves in Carnot-Carathéodory spaces possess at any point at least one tangent curve (i.e., a blow-up in the nilpotent approximation) equal to a stra…
Quantitative isoperimetric inequalities in H^n
Valentina Franceschi, Gian Paolo Leonardi, Roberto Monti
In the Heisenberg group H^n, we prove quantitative isoperimetric inequalities for Pansu's spheres, that are known to be isoperimetric under various assumptions. The inequalities ar…
Isoperimetric problem in H-type groups and Grushin spaces
Valentina Franceschi, Roberto Monti
We study the isoperimetric problem in H-type groups and Grushin spaces, emphasizing a relation between them. We prove existence, symmetry and regularity properties of isoperimetric…
Height estimate and slicing formulas in the Heisenberg group
Roberto Monti, Davide Vittone
We prove a height-estimate (distance from the tangent hyperplane) for -minima of the perimeter in the sub-Riemannian Heisenberg group. The estimate is in terms of a power of the…
Corners in non-equiregular sub-Riemannian manifolds
Enrico Le Donne, Gian Paolo Leonardi, Roberto Monti +1
We prove that in a class of non-equiregular sub-Riemannian manifolds corners are not length minimizing. This extends the results [4]. As an application of our main result we comple…
Extremal polynomials in stratified groups
Enrico Le Donne, Gian Paolo Leonardi, Roberto Monti +1
We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterizat…
Extremal curves in nilpotent Lie groups
Enrico Le Donne, Gian Paolo Leonardi, Roberto Monti +1
We classify extremal curves in free nilpotent Lie groups. The classification is obtained via an explicit integration of the adjoint equation in Pontryagin Maximum Principle. It tur…
Pseudohermitian invariants and classification of CR mappings in generalized ellipsoids
Roberto Monti, Daniele Morbidelli
We discuss the problem of classifying all local CR diffeomorphisms of a strictly pseudoconvex surface. Our method exploits the Tanaka--Webster pseudohermitian invariants, their tra…
Convex isoperimetric sets in the Heisenberg group
Roberto Monti, Matthieu Rickly
We characterize convex isoperimetric sets in the Heisenberg group endowed with horizontal perimeter. We first prove Sobolev regularity for a certain class of vector fields in the p…
Levi umbilical surfaces in complex space
R. Monti, D. Morbidelli
We define a complex connection on a real hypersurface of $\C^{n+1}$ which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify conne…