I work in the broad area of Calculus of Variations, with a particular interest in Geometric Measure Theory and Optimal Transport in sub-Riemannian Spaces such as Carnot Groups (especially the Heisenberg groups) and the Grushin plane.
A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up, 2018, with G. E. Comi, preprint (CvGmt, arXiv)
A maximal function characterization of absolutely continuous measures and Sobolev functions, 2018, with E. Bruè and Q.-H. Nguyen, preprint (CvGmt, arXiv)
Heat and entropy flows in Carnot groups, 2018, with L. Ambrosio, preprint (CvGmt, arXiv)
Symmetric double bubble in the Grushin plane, 2017, with V. Franceschi, preprint (CvGmt, arXiv)
On the monotonicity of perimeter of convex bodies, in "Journal of Convex Analysis", Vol. 25(1), 2018, to appear (CvGmt, arXiv, eprint)
Improved Lipschitz approximation of \(H\)-perimeter minimizing boundaries, 2016, with R. Monti, in "Journal de Mathématiques Pures et Appliquées", Vol. 108, no. 3, 2017, pp. 372-398 (CvGmt, arXiv, eprint)
Sobolev subspaces of nowhere bounded functions, with P. D. Lamberti, in "Real Analysis Exchange", Vol. 41(2), 2016, pp. 367–376 (arXiv, eprint)
academic works
Master Degree thesis, Intrinsic Lipschitz approximation of \(H\)-perimeter minimizing boundaries, 2016, Advisor: R. Monti, Coadvisor: L. Ambrosio (pdf)
Bachelor Degree thesis, Equazioni differenziali ordinarie - Dal Teorema di Cauchy–Lipschitz alle teorie di DiPerna–Lions e Crippa–De Lellis, 2014, Advisor: R. Monti (pdf)
Talks
Archimedes, a dinner and a theorem - A divertissement on the monotonicity of perimeter (blackboard), Pisa, April 24, 2018
Heat and entropy flows in Carnot groups(slides), Ferrara, February 27, 2018
Improved Lipschitz approximation on \(H\)-perimeter minimizing boundaries (slides), Levico Terme, February 6, 2017
On the monotonicity of perimeter of convex bodies (slides), Benevento, November 17, 2016
Workshop on Calculus of Variations and Nonlinear PDEswith a special tribute to Francesco Leonetti on the occasion of his 60th birthday, Università degli Studi del Sannio, Benevento, November 16 - 18, 2016 Contribute talk: On the monotonicity of perimeter of convex bodies (slides)