Andrea Marchese

activity

20102026

most citedThe Steiner tree problem revisited through rectifiable G-currents

29 citations · 109 across the 27 of their papers we have counts for

collaborators

34 papers

math.AP2026

Lipschitz solvability of prescribed Jacobian and divergence for singular measures

Luigi De Masi, Andrea Marchese

Let $μ$ be a finite Radon measure on an open set $Ω \subset R^{d}$ , singular with respect to the Lebesgue measure. We prove Lusin-type solvability results for the prescribed d…

math.AP2023★ 3 cited

Excess decay for minimizing hypercurrents mod $2 Q$

Camillo De Lellis, Jonas Hirsch, Andrea Marchese +2

We consider codimension $1$ area-minimizing $m$ -dimensional currents $T$ mod an even integer $p = 2 Q$ in a $C^{2}$ Riemannian submanifold $Σ$ of the Euclidean space. We prove a suitabl…

math.AP2023

Generic uniqueness for the Plateau problem

Gianmarco Caldini, Andrea Marchese, Andrea Merlo +1

Given a complete Riemannian manifold $M \subset R^{d}$ which is a Lipschitz neighbourhood retract of dimension $m + n$ , of class $C^{h, β}$ and an oriented, closed subm…

math.MG2022★ 1 cited

On the converse of Pansu's Theorem

Guido De Philippis, Andrea Marchese, Andrea Merlo +2

We provide a suitable generalisation of Pansu's differentiability theorem to general Radon measures on Carnot groups and we show that if Lipschitz maps between Carnot groups are Pa…

math.AP2022

Generic uniqueness of optimal transportation networks

Gianmarco Caldini, Andrea Marchese, Simone Steinbrüchel

We prove that for the generic boundary, in the sense of Baire categories, there exists a unique minimizer of the associated optimal branched transportation problem.

math.AP2022★ 4 cited

Fine structure of the singular set of area minimizing hypersurfaces modulo $p$

Camillo De Lellis, Jonas Hirsch, Andrea Marchese +2

Consider an area minimizing current modulo $p$ of dimension $m$ in a smooth Riemannian manifold of dimension $m + 1$ . We prove that its interior singular set is, up to a relatively c…

math.CA2021

Characterization of rectifiability via Lusin type approximation

Andrea Marchese, Andrea Merlo

We prove that a Radon measure $μ$ on $R^{n}$ can be written as $μ = \sum_{i = 0}^{n} μ_{i}$ , where each of the $μ_{i}$ is an $i$ -dimensional rectifiable measure if and only if for ever…

math.AP2021

Area minimizing hypersurfaces modulo $p$ : a geometric free-boundary problem

Camillo De Lellis, Jonas Hirsch, Andrea Marchese +2

We consider area minimizing $m$ -dimensional currents $mod (p)$ in complete $C^{2}$ Riemannian manifolds $Σ$ of dimension $m + 1$ . For odd moduli we prove that, away from a clos…

math.AP2020

Stability of optimal traffic plans in the irrigation problem

Maria Colombo, Antonio de Rosa, Andrea Marchese +2

We prove the stability of optimal traffic plans in branched transport. In particular, we show that any limit of optimal traffic plans is optimal as well. This is the Lagrangian cou…

math.AP2019★ 11 cited

Regularity of area minimizing currents mod $p$

Camillo De Lellis, Jonas Hirsch, Andrea Marchese +1

We establish a first general partial regularity theorem for area minimizing currents $mod (p)$ , for every $p$ , in any dimension and codimension. More precisely, we prove th…

math.AP2019★ 9 cited

Area minimizing currents mod $2 Q$ : linear regularity theory

Camillo De Lellis, Jonas Hirsch, Andrea Marchese +1

We establish a theory of $Q$ -valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently a…

math.AP2019

On the well-posedness of branched transportation

Maria Colombo, Antonio De Rosa, Andrea Marchese

We show in full generality the stability of optimal traffic paths in branched transport: namely we prove that any limit of optimal traffic paths is optimal as well. This solves an…

math.AP2019

The oriented mailing problem and its convex relaxation

Marcello Carioni, Andrea Marchese, Annalisa Massaccesi +2

In this note we introduce a new model for the mailing problem in branched transportation in order to allow the cost functional to take into account the orientation of the moving pa…

math.FA2018

Approximation of rectifiable $1$ -currents and weak- $*$ relaxation of the $h$ -mass

Andrea Marchese, Benedikt Wirth

Based on Smirnov's decomposition theorem we prove that every rectifiable $1$ -current $T$ with finite mass $M (T)$ and finite mass $M (\partial T)$ of its boundary $…

math.AP2018★ 9 cited

A multi-material transport problem with arbitrary marginals

Andrea Marchese, Annalisa Massaccesi, Salvatore Stuvard +1

In this paper we study general transportation problems in $R^{n}$ , in which $m$ different goods are moved simultaneously. The initial and final positions of the goods are pr…

math.AP2018

Stability for the mailing problem

Maria Colombo, Antonio De Rosa, Andrea Marchese

We prove that optimal traffic plans for the mailing problem in $R^{d}$ are stable with respect to variations of the given coupling, above the critical exponent $α = 1 - 1/ d$ , th…

math.AP2017

A multi-material transport problem and its convex relaxation via rectifiable $G$ -currents

Andrea Marchese, Annalisa Massaccesi, Riccardo Tione

In this paper we study a variant of the branched transportation problem, that we call multi-material transport problem. This is a transportation problem, where distinct commodities…

math.AP2017★ 6 cited

Quantitative minimality of strictly stable extremal submanifolds in a flat neighbourhood

Dominik Inauen, Andrea Marchese

In this paper we extend the results of "A strong minimax property of nondegenerate minimal submanifolds" by White, where it is proved that any smooth, compact submanifold, which is…

math.FA2017

A covering theorem for singular measures in the Euclidean space

Andrea Marchese

We prove that for any singular measure $μ$ on $R^{n}$ it is possible to cover $μ$ -almost every point with $n$ families of Lipschitz slabs of arbitrarily small total width. M…

math.AP2017★ 26 cited

On the lower semicontinuous envelope of functionals defined on polyhedral chains

Maria Colombo, Antonio De Rosa, Andrea Marchese +1

In this note we prove an explicit formula for the lower semicontinuous envelope of some functionals defined on real polyhedral chains. More precisely, denoting by $H \colon \mathbb…

math.AP2017★ 1 cited

Improved stability of optimal traffic paths

Maria Colombo, Antonio De Rosa, Andrea Marchese

Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree and the ner…

math.CA2016

Lipschitz functions with prescribed blowups at many points

Andrea Marchese, Andrea Schioppa

In this paper we prove generalizations of Lusin-type theorems for gradients due to Giovanni Alberti, where we replace the Lebesgue measure with any Radon measure $μ$ . We apply this…

math.AP2016

Rectifiability and upper Minkowski bounds for singularities of harmonic Q-valued maps

Camillo de Lellis, Andrea Marchese, Emanuele Spadaro +1

In this article we prove that the singular set of Dirichlet-minimizing $Q$ -valued functions is countably $(m - 2)$ -rectifiable and we give upper bounds for the $(m - 2)$ -dimensional Mi…

math.MG2016★ 1 cited

On a conjecture of Cheeger

Guido De Philippis, Andrea Marchese, Filip Rindler

This note details how a recent structure theorem for normal $1$ -currents proved by the first and third author allows to prove a conjecture of Cheeger concerning the structure of Li…

Lipschitz solvability of prescribed Jacobian and divergence for singular measures

Excess decay for minimizing hypercurrents mod 2Q

Generic uniqueness for the Plateau problem

On the converse of Pansu's Theorem

Generic uniqueness of optimal transportation networks

Fine structure of the singular set of area minimizing hypersurfaces modulo p

Characterization of rectifiability via Lusin type approximation

Area minimizing hypersurfaces modulo p: a geometric free-boundary problem

Stability of optimal traffic plans in the irrigation problem

Regularity of area minimizing currents mod p

Area minimizing currents mod 2Q: linear regularity theory

On the well-posedness of branched transportation

The oriented mailing problem and its convex relaxation

Approximation of rectifiable 1-currents and weak-∗ relaxation of the h-mass

A multi-material transport problem with arbitrary marginals

Stability for the mailing problem

A multi-material transport problem and its convex relaxation via rectifiable G-currents

Quantitative minimality of strictly stable extremal submanifolds in a flat neighbourhood

A covering theorem for singular measures in the Euclidean space

On the lower semicontinuous envelope of functionals defined on polyhedral chains

Improved stability of optimal traffic paths

Lipschitz functions with prescribed blowups at many points

Rectifiability and upper Minkowski bounds for singularities of harmonic Q-valued maps

On a conjecture of Cheeger

Excess decay for minimizing hypercurrents mod $2 Q$

Fine structure of the singular set of area minimizing hypersurfaces modulo $p$

Area minimizing hypersurfaces modulo $p$ : a geometric free-boundary problem

Regularity of area minimizing currents mod $p$

Area minimizing currents mod $2 Q$ : linear regularity theory

Approximation of rectifiable $1$ -currents and weak- $*$ relaxation of the $h$ -mass

A multi-material transport problem and its convex relaxation via rectifiable $G$ -currents