Research

My research focuses on Geometric Measure Theory and Calculus of Variations. Recently, I studied the singularities of area minimizing currents, the stability and regularty in branched transport, the structure of singular measures, and the differentiability of Lipschitz functions in metric measure spaces.

My profiles on , arXiv, cvgmt, Google Scholar, Mathscinet, Scopus, and ResearchGate.

Publications and preprints

(1) Marchese, Zanco: On a question by Corson about point finite coverings, Israel J. math. 189 (2012), 55-63. https://doi.org/10.1007/s11856-011-0126-1

(2) Marchese: Two applications of the theory of currents, PhD thesis (available at: http://cvgmt.sns.it/paper/2332/).

(3) Logaritsch, Marchese: Kirszbraun's extension theorem fails for Almgren's multiple valued functions, Arch. Math. 102 (2014), no. 5, 455-458. https://doi.org/10.1007/s00013-014-0642-4

(4) Marchese: On the building dimension of closed cones and Almgren's stratification principle, Proc. Amer. Math. Soc. 143 (2015), no. 7, 3041-3046. https://doi.org/10.1090/S0002-9939-2015-12497-5

(5) Focardi, Marchese, Spadaro: Improved estimate of the singular set of Dir-minimizing Q-valued functions via an abstract regularity result, J. Funct. Anal. 268 (2015), no. 11, 3290-3325. https://doi.org/10.1016/j.jfa.2015.02.011

(6) Marchese, Massaccesi: The Steiner tree problem revisited through rectifiable G-currents, Adv. Calc. Var. 9 (2016), no. 1, 19-39. https://doi.org/10.1515/acv-2014-0022

(7) Marchese, Massaccesi: An optimal irrigation network with infinitely many branching points, ESAIM Control Optim. Calc. Var. 22 (2016), no. 2, 543-561. https://doi.org/10.1051/cocv/2015028

(8) Alberti, Marchese: On the differentiability of Lipschitz functions with respect to measures in the Euclidean space, Geom. Funct. Anal. 26 (2016), no. 1, 1-66. https://doi.org/10.1007/s00039-016-0354-y

(9) Marchese: Lusin type theorems for Radon measures, Rend. Semin. Mat. Univ. Padova. 138 (2017), 193-207. https://doi.org/10.4171/RSMUP/138-9

(10) De Philippis, Marchese, Rindler: On a conjecture of Cheeger, Measure theory in non-smooth spaces, 145-155, Partial Differ. Equ. Meas. Theory, De Gruyter Open, Warsaw, 2017. https://doi.org/10.1515/9783110550832-004

(11) Colombo, De Rosa, Marchese, Stuvard: On the lower semicontinuous envelope of functionals defined on polyhedral chains, Nonlinear Anal. 163 (2017), 201-215. https://doi.org/10.1016/j.na.2017.08.002

(12) Marchese, Stuvard: On the structure of flat chains modulo p, Adv. Calc. Var. 11 (2018), no. 3, 309-323. https://doi.org/10.1515/acv-2016-0040

(13) Inauen, Marchese: Quantitative minimality of strictly stable extremal submanifolds in a flat neighbourhood, J. Funct. Anal. 275 (2018), no. 6, 1532-1550. https://doi.org/10.1016/j.jfa.2018.03.010

(14) Colombo, De Rosa, Marchese: Improved stability of optimal traffic paths, Calc. Var. Partial Differential Equations. 57 (2018), no. 1, Art. 28, 33 pp. https://doi.org/10.1007/s00526-017-1299-1

(15) De Lellis, Marchese, Spadaro, Valtorta: Rectifiability and upper Minkowski bounds for singularities of harmonic Q-valued maps, Comment. Math. Helv. 93 (2018), no. 4, 737–779. https://doi.org/10.4171/CMH/449

(16) Marchese: Residually many BV homeomorphisms map a null set onto a set of full measure. Proc. Roy. Soc. Edinburgh Sect. A. 149 (2019), no. 4, 1047-1059. https://doi.org/10.1017/prm.2018.104

(17) Colombo, De Rosa, Marchese: Stability for the mailing problem, J. Math. Pures Appl. 128 (2019),152–182. https://doi.org/10.1016/j.matpur.2019.01.020

(18) Marchese, Massaccesi, Tione: A multimaterial transport problem and its convex relaxation via rectifiable G-currents, SIAM J. Math. Anal. 51 (2019), no. 3, 1965-1998. https://doi.org/10.1137/17M1162858

(19) Marchese, Schioppa: Lipschitz functions with prescribed blowups at many points, Calc. Var. Partial Differential Equations. (2019), 58: 112. https://doi.org/10.1007/s00526-019-1559-3 

(20) Marchese, Wirth: Approximation of rectifiable 1-currents and weak-* relaxation of the h-mass, J. Math. Anal. Appl. 479 (2019), no. 2, 2268-2283. https://doi.org/10.1016/j.jmaa.2019.07.059

(21) Carioni, Marchese, Massaccesi, Pluda, Tione: The oriented mailing problem and its convex relaxation, Nonlinear Anal. 199 (2020), 112035. https://doi.org/10.1016/j.na.2020.112035

(22) De Lellis, Hirsch, Marchese, Stuvard: Regularity of area minimizing currents modulo p, Geom. Funct. Anal. 30 (2020), 1224–1336. https://doi.org/10.1007/s00039-020-00546-0 

(23) Colombo, De Rosa, Marchese: On the well-posedness of branched transportation, Comm. Pure Appl. Math. 74 (2021), no. 4, 833-864  https://doi.org/10.1002/cpa.21919

(24) Marchese, Massaccesi, Stuvard, Tione: A multi-material transport problem with arbitrary marginals, Calc. Var. Partial Differential Equations. (2021), 60: 88. https://doi.org/10.1007/s00526-021-01967-x 

(25) De Lellis, Hirsch, Marchese, Stuvard: Area minimizing currents mod 2Q: linear regularity theory, Comm. Pure Appl. Math. 75 (2022), no. 1, 83-127. https://doi.org/10.1002/cpa.21964 

(26) Colombo, De Rosa, Marchese, Pegon, Prouff: Stability of optimal traffic plans in the irrigation problem. Discrete Contin. Dyn. Syst. 42 (2022), no. 4, 1647-1667. https://doi.org/10.3934/dcds.2021167 

(27) Caldini, Marchese, Steinbrüchel: Generic uniqueness of optimal transportation networks. Calc. Var. Partial Differential Equations. (2023) 62:235 https://doi.org/10.1007/s00526-023-02569-5 

(28) Caldini, Marchese, Merlo, Steinbrüchel: Generic uniqueness for the Plateau problem. J. Math. Pures Appl. 181 (2024), 1-21.  https://doi.org/10.1016/j.matpur.2023.10.010 

(29) Marchese, Merlo: Characterization of rectifiability via Lusin type approximation. To appear: Analysis & PDE. Preprint: https://arxiv.org/abs/2112.15376 

(30) Marchese: A covering theorem for singular measures in the Euclidean space. Preprint: https://arxiv.org/abs/1705.05141

(31) De Lellis, Hirsch, Marchese, Spolaor, Stuvard: Area minimizing hypersurfaces modulo p: a geometric free-boundary problem. Preprint: https://arxiv.org/abs/2105.08135 

(32) De Lellis, Hirsch, Marchese, Spolaor, Stuvard: Fine structure of the singular set of area minimizing hypersurfaces modulo p. Preprint:  https://arxiv.org/abs/2201.10204 

(33) Alberti, Marchese: On the structure of flat chains with finite mass. Preprint: https://arxiv.org/abs/2311.06099 

(34) De Philippis, Marchese, Merlo, Pinamonti, Rindler: On the converse of Pansu's Theorem. Preprint: https://arxiv.org/abs/2211.06081 

(35) Alberti, Bate, Marchese: On the closability of differential operators. Preprint https://arxiv.org/abs/2311.08058 

(36) De Lellis, Hirsch, Marchese, Spolaor, Stuvard:  Excess decay for minimizing hypercurrents mod 2Q. Preprint: https://arxiv.org/abs/2308.08704