Gianmarco Caldini

I am a third-year Ph.D. student advised by Andrea Marchese and William Browder.

University of Trento, Department of Mathematics.

e-mail: gianmarco.caldini@unitn.it

Publications and preprints:

• Hausdorff measure bounds for density-Q flat singularities of minimizing integral currents (with A. Skorobogatova),

preprint arXiv:2504.19234.

• Optimal smooth approximation of integral cycles (with F. Almgren, W. Browder and C. De Lellis),

preprint arXiv:2411.17678.

• Generic uniqueness for the Plateau problem (with A. Marchese, A. Merlo and S. Steinbrüchel),

Journal de Mathématiques Pures et Appliquées, 181, 1-21, 2024.

• Generic uniqueness of optimal transportation networks (with A. Marchese and S. Steinbrüchel),

Calculus of Variations and Partial Differential Equations, 62, 235, 2023.

• On the notion of measurable utility: an order isomorphism theorem,

preprint arXiv:2301.01271.

Thesis:

• Well-posedness properties of geometric variational problems: existence, regularity and uniqueness results,

(master thesis, supervised by Andrea Marchese).