Giorgio Saracco

activity

20142026

most citedThe prescribed mean curvature equation in weakly regular domains

24 citations · 172 across the 23 of their papers we have counts for

collaborators

24 papers

math.SP2026

Convex sets with vanishing relative width and the reverse Cheeger inequality

Nicolò Cont, Gian Paolo Leonardi, Giorgio Saracco

We study the reverse Cheeger inequality, which bounds from above the ratio of the first Dirichlet Laplacian eigenvalue to the square of the Cheeger constant. We first extend this i…

math.AP2026

Spectral inequalities for weighted $p$ -Laplacians via Talenti symmetrization

Giulio Bartoli, Giorgio Saracco

We consider the weighted $p$ -Laplacian associated with a measure $μ$ that is absolutely continuous with respect to the Lebesgue measure on an open connected subset $X\subset\mathbb…

math.OC2025

A reverse isoperimetric inequality for the Cheeger constant under width constraint

Ilias Ftouhi, Ilaria Lucardesi, Giorgio Saracco

Henrot and Lucardesi, in Commun. Contemp. Math. (2024), conjectured that among planar convex sets with prescribed minimal width, the equilateral triangle uniquely maximizes the Che…

math.AP2025

On the $Γ$ -limit of weighted fractional energies

Andrea Kubin, Giorgio Saracco, Giorgio Stefani

Given $p \in [1, \infty)$ and a bounded open set $Ω \subset R^{d}$ with Lipschitz boundary, we study the $Γ$ -convergence of the weighted fractional seminorm \[ [u]_{s,p,f}^p = \in…

math.AP2024

Geometric criteria for the existence of capillary surfaces in tubes

Giorgio Saracco

We review some geometric criteria and prove a refined version, that yield existence of capillary surfaces in tubes $Ω \times R$ in a gravity free environment, in the case o…

math.AP2024★ 2 cited

Cylindrical estimates for the Cheeger constant and applications

Aldo Pratelli, Giorgio Saracco

We prove a lower bound for the Cheeger constant of a cylinder $Ω \times (0, L)$ , where $Ω$ is an open and bounded set. As a consequence, we obtain existence of minimizers for the sha…

math.FA2024★ 4 cited

On the $N$ -Cheeger problem for component-wise increasing norms

Giorgio Saracco, Giorgio Stefani

We study Cheeger and $p$ -eigenvalue partition problems depending on a given evaluation function $Φ$ for $p \in [1, \infty)$ . We prove existence and regularity of minima, relations amo…

math.MG2023★ 1 cited

On the monotonicity of weighted perimeters of convex bodies

Giorgio Saracco, Giorgio Stefani

We prove that, among weighted isotropic perimeters, only constant multiples of the Euclidean perimeter satisfy the monotonicity property on nested convex bodies. Although the analo…

math.AP2022

Isoperimetric sets and $p$ -Cheeger sets are in bijection

Marco Caroccia, Giorgio Saracco

Given an open, bounded, planar set $Ω$ , we consider its $p$ -Cheeger sets and its isoperimetric sets. We study the set-valued map $\mathfrak{V}:[\frac12,+\infty)\rightarrow\mathcal{…

math.MG2022★ 13 cited

The Cheeger problem in abstract measure spaces

Valentina Franceschi, Andrea Pinamonti, Giorgio Saracco +1

We consider non-negative $σ$ -finite measure spaces coupled with a proper functional $P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and e…

math.OC2022★ 1 cited

Optimization of the anisotropic Cheeger constant with respect to the anisotropy

Enea Parini, Giorgio Saracco

Given an open, bounded set $Ω$ in $R^{N}$ , we consider the minimization of the anisotropic Cheeger constant $h_{K} (Ω)$ with respect to the anisotropy $K$ , under a volume const…

math.AP2021

The isoperimetric problem in $2$ d domains without necks

Gian Paolo Leonardi, Giorgio Saracco

We give a complete characterization of all isoperimetric sets contained in a domain of the Euclidean plane, that is bounded by a Jordan curve and satisfies a no-neck property. Furt…

math.AP2020★ 6 cited

Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants

Vesa Julin, Giorgio Saracco

We provide a quantitative lower bound to the Cheeger constant of a set $Ω$ in both the Euclidean and the Gaussian settings in terms of suitable asymmetry indexes. We provide exampl…

math.AP2019★ 10 cited

Minimizers of the prescribed curvature functional in a Jordan domain with no necks

Gian Paolo Leonardi, Giorgio Saracco

We provide a geometric characterization of the minimal and maximal minimizer of the prescribed curvature functional $P (E) - κ ∣ E ∣$ among subsets of a Jordan domain $Ω$ with no necks o…

math.AP2019★ 14 cited

The $ε - ε^{β}$ property in the isoperimetric problem with double density, and the regularity of isoperimetric sets

Aldo Pratelli, Giorgio Saracco

We prove the validity of the $ε - ε^{β}$ property in the isoperimetric problem with double density, generalising the known properties for the case of single density…

math.AP2019

A sufficient criterion to determine planar self-Cheeger sets

Giorgio Saracco

We show a sufficient criterion to determine if a planar set $Ω$ is a minimizer of the prescribed curvature functional among all of its subsets. As a special case, we derive a suffi…

math.OC2018★ 4 cited

A discrete districting plan

Alberto Saracco, Giorgio Saracco

The outcome of elections is strongly dependent on the districting choices, making thus possible (and frequent) the gerrymandering phenomenon, i.e.\ politicians suitably changing th…

math.AP2018★ 16 cited

On the isoperimetric problem with double density

Aldo Pratelli, Giorgio Saracco

In this paper we consider the isoperimetric problem with double density in an Euclidean space, that is, we study the minimisation of the perimeter among subsets of $R^{n}$ w…

math.AP2017★ 12 cited

Two examples of minimal Cheeger sets in the plane

Gian Paolo Leonardi, Giorgio Saracco

We construct two minimal Cheeger sets in the Euclidean plane, i.e. unique minimizers of the ratio "perimeter over area" among their own measurable subsets. The first one gives a co…

math.AP2017★ 17 cited

Rigidity and trace properties of divergence-measure vector fields

Gian Paolo Leonardi, Giorgio Saracco

We consider a $φ$ -rigidity property for divergence-free vector fields in the Euclidean $n$ -space, where $φ (t)$ is a non-negative convex function vanishing only at $t = 0$ . We show th…

math.AP2017★ 21 cited

The Cheeger constant of a Jordan domain without necks

Gian Paolo Leonardi, Robin Neumayer, Giorgio Saracco

We show that the maximal Cheeger set of a Jordan domain $Ω$ without necks is the union of all balls of radius $r = h (Ω)^{- 1}$ contained in $Ω$ . Here, $h (Ω)$ denotes the Cheeger con…

math.FA2016★ 14 cited

Weighted Cheeger sets are domains of isoperimetry

Giorgio Saracco

We consider a generalization of the Cheeger problem in a bounded, open set $Ω$ by replacing the perimeter functional with a Finsler-type surface energy and the volume with suitable…

math.AP2016★ 24 cited

The prescribed mean curvature equation in weakly regular domains

Gian Paolo Leonardi, Giorgio Saracco

We show that the characterization of existence and uniqueness up to vertical translations of solutions to the prescribed mean curvature equation, originally proved by Giusti in the…

math.MG2014★ 13 cited

On the generalized Cheeger problem and an application to 2d strips

Aldo Pratelli, Giorgio Saracco

In this paper we consider the generalization of the Cheeger problem which comes by considering the ratio between the perimeter and a certain power of the volume. This generalizatio…

Convex sets with vanishing relative width and the reverse Cheeger inequality

Spectral inequalities for weighted p-Laplacians via Talenti symmetrization

A reverse isoperimetric inequality for the Cheeger constant under width constraint

On the Γ-limit of weighted fractional energies

Geometric criteria for the existence of capillary surfaces in tubes

Cylindrical estimates for the Cheeger constant and applications

On the N-Cheeger problem for component-wise increasing norms

On the monotonicity of weighted perimeters of convex bodies

Isoperimetric sets and p-Cheeger sets are in bijection

The Cheeger problem in abstract measure spaces

Optimization of the anisotropic Cheeger constant with respect to the anisotropy

The isoperimetric problem in 2d domains without necks

Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants

Minimizers of the prescribed curvature functional in a Jordan domain with no necks

The ε−εβ property in the isoperimetric problem with double density, and the regularity of isoperimetric sets

A sufficient criterion to determine planar self-Cheeger sets

A discrete districting plan

On the isoperimetric problem with double density

Two examples of minimal Cheeger sets in the plane

Rigidity and trace properties of divergence-measure vector fields

The Cheeger constant of a Jordan domain without necks

Weighted Cheeger sets are domains of isoperimetry

The prescribed mean curvature equation in weakly regular domains

On the generalized Cheeger problem and an application to 2d strips

Spectral inequalities for weighted $p$ -Laplacians via Talenti symmetrization

On the $Γ$ -limit of weighted fractional energies

On the $N$ -Cheeger problem for component-wise increasing norms

Isoperimetric sets and $p$ -Cheeger sets are in bijection

The isoperimetric problem in $2$ d domains without necks

The $ε - ε^{β}$ property in the isoperimetric problem with double density, and the regularity of isoperimetric sets