G. P. Leonardi:
Infiltrations in immiscible fluids systems
Proceedings of the Royal Society of Edinburgh N. 131A, p. 425-436, 2001

G. P. Leonardi, I. Tamanini:
Metric spaces of partitions, and Caccioppoli partitions
Adv. Math. Sci. Appl. Vol. 12, N. 2, p. 725-753, 2002

G. P. Leonardi:
Partitions with prescribed mean curvatures
Manuscripta Math. Vol. 107, N. 1, p. 111-133, 2002

G. P. Leonardi, S. Rigot:
Isoperimetric sets in Carnot groups
Houston J. Math. (Accepted Paper) 2002

G. P. Leonardi:
Gamma-convergence of constrained Dirichlet functionals
Boll. UMI Vol. 6-B, N. 8, p. 339-351, 2003

G. P. Leonardi, S. Masnou:
On the isoperimetric problem in the Heisenberg group ${\mathbf{H^n}}$
Annali di Mat. Pura Appl. Vol. 184, p. 533-553, 2005

G. P. Leonardi, P. Tilli:
On a constrained variational problem in the vector-valued case
J. Math. Pures Appl. Vol. 85, p. 251-268, 2006

G. P. Leonardi, R. Monti:
End-point equations and regularity of sub-Riemannian geodesics
GAFA (Accepted Paper) 2006

G. P. Leonardi, S. Masnou:
Locality of the mean curvature of rectifiable varifolds
Adv. Calc. Var. Vol. 2, N. 1, p. 17-42, 2009

G. P. Leonardi, V. Magnani:
Intersections of intrinsic submanifolds in the Heisenberg group
J. Math. Anal. Appl.  Vol.  378, N. 1, p. 98108, 2011

G. P. Leonardi, S. Rigot, D. Vittone:
Isodiametric sets in the Heisenberg group
Rev. Mat. Iberoam. Vol. 28, N. 4, p. 999-1024, 2012

M. Cicalese, G. P. Leonardi:
A Selection Principle for the Sharp Quantitative Isoperimetric
  Inequality
Arch. Rat. Mech. Anal. Vol. 206, N. 2, p. 617-643, 2012

E. Le Donne, G. P. Leonardi, R. Monti, D. Vittone:
Extremal curves in nilpotent Lie groups
GAFA Geometric and Functional Analysis Vol. 23, N. 4, p. 1371--1401, 2013

M. Cicalese, G. P. Leonardi:
Best constants for the isoperimetric inequality in quantitative form
J. Eur. Math. Soc. (JEMS) Vol. 15, N. 3, p. 1101-1129, 2013

V. Franceschi, G. P. Leonardi, R. Monti:
Quantitative isoperimetric inequalities in $\mathbb H ^n$
Calc. Var. Partial Differential Equations Vol. 54, N. 3, p. 3229-3239, 2015

E. Le Donne, G. P. Leonardi, R. Monti, D. Vittone:
Corners in non-equiregular sub-Riemannian manifolds
ESAIM Control Optim. Calc. Var. Vol. 21, N. 3, p. 625--634, 2015

G. P. Leonardi:
An overview on the Cheeger problem
(Preprint) 2015

G. P. Leonardi, F. Maggi:
Improved convergence theorems for bubble clusters. II. The three-dimensional case
Indiana U Math Journal (Accepted Paper) 2015

B. Buet, G. P. Leonardi:
Recovering measures from approximate values on balls
Ann. Acad. Sci. Fenn. (Accepted Paper) Vol. 41, p. 1--26, 2016

B. Buet, G. P. Leonardi, S. Masnou:
A varifold approach to surface approximation
(Preprint) 2016

G. P. Leonardi, A. Pratelli:
On the Cheeger sets in strips and non-convex domains
Calc. Var. PDE 2016

M. Cicalese, G. P. Leonardi, F. Maggi:
Improved convergence theorems for bubble clusters. I. The planar case
Indiana U Math Journal Vol. 65, p. 1979-2050, 2016

M. Cicalese, G. P. Leonardi, F. Maggi:
Sharp stability inequalities for planar double bubbles
Interfaces and Free Boundaries Vol. 19, N. 3, p. 305350, 2017

G. P. Leonardi, R. Neumayer, G. Saracco:
The Cheeger constant of a Jordan domain without necks
Calc. Var. Partial Differential Equations Vol. 56, N. 6, p. 164, 2017

E. Le Donne, G. P. Leonardi, R. Monti, D. Vittone:
Extremal polynomials in stratified groups
Comm. Anal. and Geom. Vol. 26, p. 723757, 2018

D. Krejcirik, G. P. Leonardi, P. Vlachopulos:
The Cheeger constant of curved tubes
Arkiv der Mathematik 2018

G. P. Leonardi, M. Ritoré, E. Vernadakis:
Isoperimetric inequalities in unbounded convex bodies
Mem. AMS (Accepted Paper) 2018

G. P. Leonardi, G. Saracco:
Two examples of minimal Cheeger sets in the plane
Ann. Mat. Pura Appl. (4) Vol. 197, N. 5, p. 1511, 2018

G. P. Leonardi, G. Saracco:
The prescribed mean curvature equation in weakly regular domains
NoDEA Nonlinear Differential Equations Appl. Vol. 25, N. 2, p. 9, 2018

M. Cicalese, G. P. Leonardi:
Maximal fluctuations on periodic lattices: an approach via quantitative Wulff inequalities
Commun. Math. Phys. Vol. 375, p. 19311944, 2019

G. P. Leonardi, G. Saracco:
Minimizers of the prescribed curvature functional in a Jordan domain with no necks
ESAIM Control Optim. Calc. Var. Vol. 26, p. 76, 2020

G. P. Leonardi, G. Saracco:
The isoperimetric problem in $2$d domains without necks
Calc. Var. Partial Differential Equations Vol. 61, N. 2, p. 56, 2022

G. P. Leonardi, G. Saracco:
Rigidity and trace properties of divergence-measure vector fields
Adv. Calc. Var. Vol. 15, N. 1, p. 133--149, 2022

L. Benini, G. P. Leonardi, M. Spallanzani:
Training Quantised Neural Networks with STE Variants: the Additive Noise  Annealing Algorithm
IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (Proceedings) 2022

G. E. Comi, G. P. Leonardi:
The prescribed mean curvature measure equation in non-parametric form
(preprint) 2023

M. Cicalese, L. Kreutz, G. P. Leonardi:
Emergence of Wulff-Crystals from atomistic systems on the FCC and HCP lattices
Comm. Math. Phys. Vol. 402, N. 3, p. 29312978, 2023

M. Datres, A. Figalli, G. P. Leonardi, D. Sutter:
A Two-Scale Complexity Measure for Deep Learning Models
(preprint) 2024

G. P. Leonardi, G. Vianello:
A Vertex-Skipping property for almost-minimizers of the relative perimeter in convex sets
(Preprint) 2024