29 citations · 109 across the 27 of their papers we have counts for
20 papers · 1 filter
Lipschitz solvability of prescribed Jacobian and divergence for singular measures
Luigi De Masi, Andrea Marchese
Let be a finite Radon measure on an open set , singular with respect to the Lebesgue measure. We prove Lusin-type solvability results for the prescribed d…
Excess decay for minimizing hypercurrents mod
Camillo De Lellis, Jonas Hirsch, Andrea Marchese +2
We consider codimension area-minimizing -dimensional currents mod an even integer in a Riemannian submanifold of the Euclidean space. We prove a suitabl…
Generic uniqueness for the Plateau problem
Gianmarco Caldini, Andrea Marchese, Andrea Merlo +1
Given a complete Riemannian manifold which is a Lipschitz neighbourhood retract of dimension , of class and an oriented, closed subm…
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.
Fine structure of the singular set of area minimizing hypersurfaces modulo
Camillo De Lellis, Jonas Hirsch, Andrea Marchese +2
Consider an area minimizing current modulo of dimension in a smooth Riemannian manifold of dimension . We prove that its interior singular set is, up to a relatively c…
Area minimizing hypersurfaces modulo : a geometric free-boundary problem
Camillo De Lellis, Jonas Hirsch, Andrea Marchese +2
We consider area minimizing -dimensional currents in complete Riemannian manifolds of dimension . For odd moduli we prove that, away from a clos…
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…
Regularity of area minimizing currents mod
Camillo De Lellis, Jonas Hirsch, Andrea Marchese +1
We establish a first general partial regularity theorem for area minimizing currents , for every , in any dimension and codimension. More precisely, we prove th…
Area minimizing currents mod : linear regularity theory
Camillo De Lellis, Jonas Hirsch, Andrea Marchese +1
We establish a theory of -valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently a…
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…
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…
A multi-material transport problem with arbitrary marginals
Andrea Marchese, Annalisa Massaccesi, Salvatore Stuvard +1
In this paper we study general transportation problems in , in which different goods are moved simultaneously. The initial and final positions of the goods are pr…
Stability for the mailing problem
Maria Colombo, Antonio De Rosa, Andrea Marchese
We prove that optimal traffic plans for the mailing problem in are stable with respect to variations of the given coupling, above the critical exponent , th…
A multi-material transport problem and its convex relaxation via rectifiable -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…
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…
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…
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…
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 -valued functions is countably -rectifiable and we give upper bounds for the -dimensional Mi…
On the structure of flat chains modulo
Andrea Marchese, Salvatore Stuvard
In this paper, we prove that every equivalence class in the quotient group of integral -currents modulo in Euclidean space contains an integral current, with quantitative es…
Improved estimate of the singular set of Dir-minimizing Q-valued functions via an abstract regularity result
Matteo Focardi, Andrea Marchese, Emanuele Spadaro
In this note we prove an abstract version of a recent quantitative stratifcation priciple introduced by Cheeger and Naber (Invent. Math., 191 (2013), no. 2, 321-339; Comm. Pure App…