29 citations · 109 across the 27 of their papers we have counts for
6 papers · 1 filter
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…
On the building dimension of closed cones and Almgren's stratification principle
Andrea Marchese
In this paper we disprove a conjecture stated in [4] on the equality of two notions of dimension for closed cones. Moreover, we answer in the negative to the following question, ra…
On the differentiability of Lipschitz functions with respect to measures in the Euclidean space
Giovanni Alberti, Andrea Marchese
Rademacher theorem states that every Lipschitz function on the Euclidean space is differentiable almost everywhere, where "almost everywhere" refers to the Lebesgue measure. In thi…