8 papers
Structural identification in general crystalline systems via Voronoi cell topology
Emanuel A. Lazar, Chris H. Rycroft
Widely used methods for identifying crystal structure in atomistic simulations are limited in practice to a handful of simple structures, leaving many important crystalline systems…
On smooth approximation of integral cycles mod 2
Gianmarco Caldini
We prove that every mod 2 integral cycle in a Riemannian manifold can be approximated in flat norm by a cycle which is a smooth submanifold of nearly the same…
Hausdorff measure bounds for density- flat singularities of minimizing integral currents
Gianmarco Caldini, Anna Skorobogatova
In this article we prove that the set of flat singular points of locally highest density of area-minimizing integral currents of dimension and general codimension in a smooth R…
Optimal smooth approximation of integral cycles
Fredrick Almgren, William Browder, Gianmarco Caldini +1
In this article we prove that each integral cycle in an oriented Riemannian manifold can be approximated in flat norm by an integral cycle in the same homology cl…
Generic uniqueness for the Plateau problem
Gianmarco Caldini, Andrea Marchese, Andrea Merlo +1
Given a complete Riemannian manifold which is a Lipschitz neighbourhood retract of dimension , of class and an oriented, closed subm…
On the notion of measurable utility on a connected and separable topological space: an order isomorphism theorem
Gianmarco Caldini
The aim of this article is to define a notion of cardinal utility function called measurable utility and to define it on a connected and separable subset of a weakly ordered topolo…
Well-posedness properties of geometric variational problems: existence, regularity and uniqueness results
Gianmarco Caldini
This thesis is devoted to the study of well-posedness properties of some geometric variational problems: existence, regularity and uniqueness of solutions. We study two specific pr…
Generic uniqueness of optimal transportation networks
Gianmarco Caldini, Andrea Marchese, Simone Steinbrüchel
We prove that for the generic boundary, in the sense of Baire categories, there exists a unique minimizer of the associated optimal branched transportation problem.