Research Papers

An updated list is always available on my personal page on the cvgmt preprint server along with the preprints of the papers.

Should you need a final version for personal use, as appeared in the journal, feel free to ask me one by writing me an e-mail.

Typos:  

• In [Theorem A, 6] there is a typo; the preprint contains now the amended statement.

• In [Equation (2.2), 12] defining the index ζ(Ω) the rescaling factor is missing (as otherwise the quantitative inequality (2.5) would be false as written). Consequently, in the proof of Theorem 2.1 and in the following example several renormalization constants are missing. The preprint contains now the amended statement.

• In [Lemma 4.17, 20] the hypothesis that the superlevel sets considered have positive Lebesgue measure is missing. The preprint contains now the amended statement.

Publications

[21] A. Pratelli and G. Saracco, Cylindrical estimates for the Cheeger constant and applications, J. Math Pures Appl. (9) 194:103633, 2025

[20] G. Saracco and G. Stefani,  On the N-Cheeger problem for component-wise increasing norms, J. Math Pures Appl. (9) 189:103593, 2024

[19] G. Saracco and G. Stefani, On the monotonicity of weighted perimeters of convex bodies, Math. Nachr. 297(4):1444–1450, 2024

[18] G. Saracco, Geometric criteria for the existence of capillary surfaces in tubes, Expo. Math. 42(3):125547, 2024

[17] V. Franceschi, A. Pinamonti, G. Saracco, and G. Stefani, The Cheeger problem in abstract measure spaces, J. London Math. Soc. (2) 119(1):e12840, 2024 *Top cited article - Wiley (top 10 most-cited articles published by the journal in 2023) --- *Top viewed article - Wiley (top 10 most-viewed articles published by the journal in 2023)* * 

[16] E. Parini and G. Saracco, Optimization of the anisotropic Cheeger constant with respect to the anisotropy, Canad. Math. Bull., 66(3):1030–1043, 2023

[15] M. Caroccia and G. Saracco, Isoperimetric sets and $p$-Cheeger sets are in bijection, J. Geom. Anal., 33(4):129, 2023

[14] G. P. Leonardi and G. Saracco, Rigidity and trace properties of divergence-measure vector fields, Adv. Calc. Var., 15(1):133–149, 2022

[13] G. P. Leonardi and G. Saracco, The isoperimetric problem in 2d domains without necks, Calc. Var. Partial Differential Equations, 61(2):56, 2022

[12] V. Julin and G. Saracco, Quantitative lower bounds to the Euclidean and Gaussian Cheeger constants, Ann. Fenn. Math., 46(2):1071–1087, 2021

[11] G. Saracco, A sufficient criterion to determine planar self-Cheeger sets, J. Convex Anal., 28(3):951–958, 2021

[10] G. P. Leonardi and G. Saracco,  Minimizers of the prescribed curvature functional in a Jordan domain with no necks, ESAIM Control Optim. Calc. Var., 26:76, 2020

[9] A. Saracco and G. Saracco, Matematica ed elezioni, paradossi e problemi elettorali, Mat. Cult. Soc. Riv. Unione Mat. Ital. (I), 5(1):17–31, 2020

[8] A. Pratelli and G. Saracco, The ε-ε^β property in the isoperimetric problem with double density, and the regularity of isoperimetric sets, Adv. Nonlinear Stud., 20(3):539–555, 2020

[7] A. Saracco and G. Saracco, A discrete districting plan, Netw. Heterog. Media, 14(4):771–788, 2019

[6] A. Pratelli and G. Saracco, On the isoperimetric problem with double density, Nonlinear Anal., 177(Part B):733–752, 2018

[5] G. P. Leonardi and G. Saracco, Two examples of minimal Cheeger sets in the plane, Ann. Mat. Pura Appl. (4), 197(5):1511–1531, 2018

[4] G. Saracco, Weighted Cheeger sets are domains of isoperimetry, Manuscripta Math., 156(3-4):371–381, 2018

[3] G. P. Leonardi and G. Saracco, The prescribed mean curvature equation in weakly regular domains, NoDEA Nonlinear Differential Equations Appl., 25(2):9, 2018

[2] G. P. Leonardi, R. Neumayer, and G. Saracco, The Cheeger constant of a Jordan domain without necks, Calc. Var. Partial Differential Equations, 56(6):164, 2017

[1] A. Pratelli and G. Saracco, On the generalized Cheeger problem and an application to 2D strips, Rev. Mat. Iberoam., 33(1):219–237, 2017