A. Marchese, C. Zanco:
On a question by Corson about point-finite coverings
Israel J. math. 2012
A. Marchese:
Two applications of the Theory of Currents
(Phd Thesis) 2013
A. Marchese:
On the building dimension of closed cones and Almgrens stratification principle.
Proc. Amer. Math. Soc. (Accepted Paper) 2013
P. Logaritsch, A. Marchese:
Kirszbraun's extension theorem fails for Almgren's multiple valued functions
Arch. Math Vol. 102, N. 5, p. 455-458, 2014
A. Marchese, A. Massaccesi:
An optimal irrigation network with infinitely many branching points
ESAIM: COCV (ESAIM Control Optim. Calc. Var.) 2014
A. Marchese:
Lusin type theorems for Radon measures
(Rend. Semin. Mat. Univ. Padova) 2015
M. Focardi, A. Marchese, E. Spadaro:
Improved estimate of the singular set of Dir-minimizing Q-valued functions via an abstract regularity result
Journal of Functional Analysis Vol. 268, p. 3290--3325, 2015
A. Marchese, A. Massaccesi:
The Steiner tree problem revisited through rectifiable $G$-currents
Advances in Calculus of Variations Vol. 9, N. 1, p. 19-39, 2016
G. Alberti, A. Marchese:
On the differentiability of Lipschitz functions with respect to measures in the Euclidean space
Geom. Funct. Anal. (GAFA) Vol. 26, N. 1, p. 1-66, 2016
G. De Philippis, A. Marchese, F. Rindler:
On a conjecture of Cheeger
(Accepted Paper) 2016
A. Marchese, A. Schioppa:
Lipschitz functions with prescribed blowups at many points
Calc. Var. Partial Differential Equations 2016
A. Marchese:
On the structure of singular measures in the Euclidean space
(Preprint) 2017
A. Marchese:
Residually many BV homeomorphisms map a null set in a set of full measure
Proc. Roy. Soc. Edinburgh Sect. A (Accepted Paper) 2017
M. Colombo, A. De Rosa, A. Marchese, S. Stuvard:
On the lower semicontinuous envelope of functionals defined on polyhedral chains
Nonlinear Analysis Vol. 163C, p. 201-215, 2017
D. Inauen, A. Marchese:
Quantitative minimality of strictly stable minimal submanifolds in a small flat neighbourhood
J. Funct. Anal. 2017
A. Marchese, S. Stuvard:
On the structure of flat chains modulo $p$
Adv. Calc. Var. Vol. 11, N. 3, p. 309-323, 2018
A. Marchese, B. Wirth:
Approximation of rectifiable $1$-currents and weak-$\ast$ relaxation of the $h$-mass
J. Math. Anal. Appl. 2018
C. De Lellis, A. Marchese, E. Spadaro, D. Valtorta:
Rectifiability and upper Minkowski bounds for singularities of harmonic $Q$-valued maps
Comm. Math. Helv. Vol. 93, N. 4, p. 737-779, 2018
M. Colombo, A. De Rosa, A. Marchese:
Improved stability of optimal traffic paths
Calc. Var. Partial Differential Equations 2018
M. Colombo, A. De Rosa, A. Marchese:
Stability for the mailing problem
J. Math. Pures Appl. 2019
A. Marchese, A. Massaccesi, R. Tione:
A multi-material transport problem and its convex relaxation via rectifiable G-currents
SIAM J. Math. Anal. Vol. 51, N. 3, p. 1965-1998, 2019
C. De Lellis, J. Hirsch, A. Marchese, S. Stuvard:
Regularity of area minimizing currents mod $p$
Geom. Funct. Anal. Vol. 30, N. 5, p. 1224-1336, 2020
M. Carioni, A. Marchese, A. Massaccesi, A. Pluda, R. Tione:
The oriented mailing problem and its convex relaxation
Nonlinear Anal. Vol. 199, 2020
M. Colombo, A. De Rosa, A. Marchese:
On the well-posedness of branched transportation
Comm. Pure App. Math. 2021
A. Marchese, A. Massaccesi, S. Stuvard, R. Tione:
A multi-material transport problem with arbitrary marginals
Calc. Var. Partial Differential Equations Vol. 60, N. 88, p. 1-49, 2021
C. De Lellis, J. Hirsch, A. Marchese, L. Spolaor, S. Stuvard:
Area minimizing hypersurfaces modulo $p$: a geometric free-boundary problem
(Submitted Paper) 2021
A. Marchese, A. Merlo:
Characterization of rectifiability via Lusin type approximation
Analysis & PDE (Accepted Paper) 2021
C. De Lellis, J. Hirsch, A. Marchese, S. Stuvard:
Area minimizing currents mod $2Q$: linear regularity theory
Comm. Pure Appl. Math. Vol. 75, N. 1, p. 83-127, 2022
G. De Philippis, A. Marchese, A. Merlo, A. Pinamonti, F. Rindler:
On the converse of Pansu's Theorem
(Submitted Paper) 2022
G. Caldini, A. Marchese, S. Steinbrüchel:
Generic uniqueness of optimal transportation networks
Calc. Var. PDE (Accepted Paper) 2022
M. Colombo, A. De Rosa, A. Marchese, P. Pegon, A. Prouff:
Stability of optimal traffic plans in the irrigation problem
Discrete and Continuous Dynamical Systems Vol. 2, N. 4, p. 1647-1667, 2022
G. Alberti, A. Marchese:
On the structure of flat chains with finite mass
(Preprint) 2022
C. De Lellis, J. Hirsch, A. Marchese, L. Spolaor, S. Stuvard:
Fine structure of the singular set of area minimizing hypersurfaces modulo $p$
(Submitted Paper) 2022
G. Alberti, D. Bate, A. Marchese:
On the closability of differential operators
(Preprint) 2023
G. Caldini, A. Marchese, A. Merlo, S. Steinbrüchel:
Generic uniqueness for the Plateau problem
J. Math. Pures Appl. (Accepted Paper) 2023
C. De Lellis, J. Hirsch, A. Marchese, L. Spolaor, S. Stuvard:
Excess decay for minimizing hypercurrents mod $2Q$
(Submitted Paper) 2023
A. Marchese, A. Merlo:
A simple proof of the $1$-dimensional flat chain conjecture
(Preprint) 2024