Giacomo Del Nin

activity

20182026

most citedDegenerate elastic networks

4 citations · 7 across the 15 of their papers we have counts for

collaborators

18 papers

math.AP2026

Boundary rectifiability and compactness of integral currents via $B V$ functions

Giacomo Del Nin

We present a new proof that an integer rectifiable current with finite mass, and whose boundary has also finite mass, is integral. We deduce the result from De Giorgi's structure t…

math.AP2026

Turbulent Dynamos on Bounded Domains and Their Generalization to the Geometric Transport Equation

Giacomo Del Nin, Daniel Faraco, Sauli Lindberg +1

For any smooth bounded domain $Ω \subset R^{3}$ , we construct a divergence-free velocity field $u \in L_{t}^{1} W^{1, p} (Ω)$ for all $p < \infty$ , and magnetic fields $B^ε\in L_t^…

math.CA2025

Marstrand's density theorem for arbitrary norms in the plane

Giacomo Del Nin, Andrea Merlo

We show that if a non-trivial measure in the plane admits, at almost every point, positive and finite $α$ -dimensional density with respect to some norm, then $α$ must be an integer…

math.AP2025

Well-posedness of the transport of normal currents by time-dependent vector fields

Paolo Bonicatto, Giacomo Del Nin

We prove existence and uniqueness for the transport equation for currents (Geometric Transport Equation) when the driving vector field is time-dependent, Lipschitz in space and mer…

math.AP2025

The square sticky disk: crystallization and Gamma-convergence to the octagonal anisotropic perimeter

Giacomo Del Nin, Lucia De Luca

We consider a variant of the sticky disk energy where distances between particles are evaluated through the sup norm $∥ \cdot ∥_{\infty}$ in the plane. We first prove crystal…

math.AP2024

Approximation of divergence-free vector fields vanishing on rough planar sets

Giacomo Del Nin, Bian Wu

Given any divergence-free vector field of Sobolev class $W_{0}^{m, p} (Ω)$ in a bounded open subset $Ω \subset R^{2}$ , we are interested in approximating it in the $W^{m, p}$ norm…

math.AP2024

Local Poincaré constants and mean oscillation functionals for $B V$ functions

Adolfo Arroyo-Rabasa, Paolo Bonicatto, Giacomo Del Nin

We introduce the concept of local Poincaré constant of a $B V$ function as a tool to understand the relation between its mean oscillation and its total variation at small scales. Th…

math-ph2023

A crystallization result in two dimensions for a soft disc affine potential

Giacomo Del Nin, Lucia De Luca

We prove finite crystallization for particles in the plane interacting through a soft disc potential, as originally shown by C. Radin \cite{Radin_soft}. We give an alternative proo…

math.AP2023★ 1 cited

Existence and uniqueness for the transport of currents by Lipschitz vector fields

Paolo Bonicatto, Giacomo Del Nin, Filip Rindler

This work establishes the existence and uniqueness of solutions to the initial-value problem for the geometric transport equation $$ \frac{\mathrm{d}}{\mathrm{d} t}T_t+\mathcal{L}_…

math.DG2022

Rigidity of mass-preserving $1$ -Lipschitz maps from integral current spaces into $R^{n}$

Giacomo Del Nin, Raquel Perales

We prove that given an $n$ -dimensional integral current space and a $1$ -Lipschitz map, from this space onto the $n$ -dimensional Euclidean ball, that preserves the mass of the curre…

math.AP2022★ 2 cited

Transport of currents and geometric Rademacher-type theorems

Paolo Bonicatto, Giacomo Del Nin, Filip Rindler

The transport of many kinds of singular structures in a medium, such as vortex points/lines/sheets in fluids, dislocation loops in crystalline plastic solids, or topological singul…

math.AP2021

Representation of the total variation as a $Γ$ -limit of $B M O$ -type seminorms

Adolfo Arroyo-Rabasa, Paolo Bonicatto, Giacomo Del Nin

We address a question raised by Ambrosio, Bourgain, Brezis, and Figalli, proving that the $Γ$ -limit, with respect to the $L_{loc}^{1}$ topology, of a family of $B M O$ -type seminor…

math.MG2021

Decomposition of integral metric currents

Paolo Bonicatto, Giacomo Del Nin, Enrico Pasqualetto

In the setting of complete metric spaces, we prove that integral currents can be decomposed as a sum of indecomposable components. In the special case of one-dimensional integral c…

math.CA2021

Endpoint Fourier restriction and unrectifiability

Giacomo Del Nin, Andrea Merlo

We show that if a measure of dimension $s$ on $R^{d}$ admits $(p, q)$ Fourier restriction for some endpoint exponents allowed by its dimension, namely $q = \frac{s}{d} p^{'}$ for…

math.MG2021

Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings

Giacomo Del Nin, Mircea Petrache

We prove discrete-to-continuum convergence of interaction energies defined on lattices in the Euclidean space (with interactions beyond nearest neighbours) to a crystalline perimet…

math.CA2020

Rectifiability of the jump set of locally integrable functions

Giacomo Del Nin

In this note we show that for every measurable function on $R^{n}$ the set of points where the blowup exists and is not constant is $(n - 1)$ -rectifiable. In particular, for e…

math.OC2019★ 4 cited

Degenerate elastic networks

Giacomo Del Nin, Alessandra Pluda, Marco Pozzetta

We minimize a linear combination of the Willmore and the length functional among networks in $R^{d}$ belonging to a given class determined by the number of curves, the order…

math.OC2018

Sticky-disk limit of planar $N$ -bubbles

Giacomo Del Nin

We study planar $N$ -clusters that minimize, under an area constraint, a weighted perimeter $P_{ε}$ depending on a small parameter $ε > 0$ . Specifically we weight $2…

Boundary rectifiability and compactness of integral currents via BV functions

Turbulent Dynamos on Bounded Domains and Their Generalization to the Geometric Transport Equation

Marstrand's density theorem for arbitrary norms in the plane

Well-posedness of the transport of normal currents by time-dependent vector fields

The square sticky disk: crystallization and Gamma-convergence to the octagonal anisotropic perimeter

Approximation of divergence-free vector fields vanishing on rough planar sets

Local Poincaré constants and mean oscillation functionals for BV functions

A crystallization result in two dimensions for a soft disc affine potential

Existence and uniqueness for the transport of currents by Lipschitz vector fields

Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into Rn

Transport of currents and geometric Rademacher-type theorems

Representation of the total variation as a Γ-limit of BMO-type seminorms

Decomposition of integral metric currents

Endpoint Fourier restriction and unrectifiability

Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings

Rectifiability of the jump set of locally integrable functions

Degenerate elastic networks

Sticky-disk limit of planar N-bubbles

Boundary rectifiability and compactness of integral currents via $B V$ functions

Local Poincaré constants and mean oscillation functionals for $B V$ functions

Rigidity of mass-preserving $1$ -Lipschitz maps from integral current spaces into $R^{n}$

Representation of the total variation as a $Γ$ -limit of $B M O$ -type seminorms

Sticky-disk limit of planar $N$ -bubbles