29 citations · 37 across the 8 of their papers we have counts for
8 papers
On the structure of flat chains with finite mass
Giovanni Alberti, Andrea Marchese
We prove that every flat chain with finite mass in with coefficients in a normed abelian group is the restriction of a normal -current to a Borel set. We dedu…
On a conjecture of Cheeger
Guido De Philippis, Andrea Marchese, Filip Rindler
This note details how a recent structure theorem for normal -currents proved by the first and third author allows to prove a conjecture of Cheeger concerning the structure of Li…
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…
The Steiner tree problem revisited through rectifiable G-currents
Andrea Marchese, Annalisa Massaccesi
The Steiner tree problem can be stated in terms of finding a connected set of minimal length containing a given set of finitely many points. We show how to formulate it as a mass-m…
Kirszbraun's extension theorem fails for Almgren's multiple valued functions
Philippe Logaritsch, Andrea Marchese
We show that there is no analog of Kirszbraun's extension theorem for Almgren's multiple valued functions.
An optimal irrigation network with infinitely many branching points
Andrea Marchese, Annalisa Massaccesi
The Gilbert-Steiner problem is a mass transportation problem, where the cost of the transportation depends on the network used to move the mass and it is proportional to a certain…