Calculus of Variations, Geometric Measure Theory, Convex Geometry, Viscosity solutions of PDE’s, Mathematical models in elastic and fracture mechanics.

Papers

Published or accepted

• MARIO SANTILLI. Rectifiability and approximate differentiability of higher order for sets. Indiana Univ. Math. J. 68 (2019), 1013–1046.
• ULRICH MENNE, MARIO SANTILLI. A geometric second-order-rectifiable stratification for closed subsets of Euclidean space. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19(3) (2019), 1185-1198.
• MARIO SANTILLI. Fine properties of the curvature of arbitrary closed sets. Ann. Mat. Pura Appl. (4), 199, (2020), no. 4, 1431-1456.
• MARIO SANTILLI. Normal bundle and Almgren’s geometric inequality for singular varieties of bounded mean curvature. Bull. Math. Sci. 10(1) 2050008, 24, 2020.
• ANTONIO DE ROSA, SŁAWOMIR KOLASINSKI ´ , MARIO SANTILLI Uniqueness of critical points of the anisotropic isoperimetric problem for finite perimeter sets. Arch Rational Mech Anal 238, 1157–1198 (2020). https://doi.org/10.1007/s00205-020-01562-y

Preprints

• MARIO SANTILLI. Second order rectifiability of varifolds of bounded mean curvature. Submitted. https://arxiv.org/abs/1907.02792
• MARIO SANTILLI. Distance functions with dense singular sets. Submitted. https://arxiv.org/abs/2007.08959
• MARIO SANTILLI. Uniqueness of singular convex hypersurfaces with lower bounded k-th mean curvature