Andrea Merlo

collaborators

4 papers

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.DG2025

Frobenius theorem and fine structure of tangency sets to non-involutive distributions

Giovanni Alberti, Annalisa Massaccesi, Andrea Merlo

In this paper we provide a complete answer to the question whether Frobenius' Theorem can be generalized to surfaces below the $C^{1, 1}$ threshold. We study the fine structure of t…

math.AP2025

Layer potentials for elliptic operators with DMO-type coefficients: big pieces $T b$ theorem, quantitative rectifiability, and free boundary problems

Andrea Merlo, Mihalis Mourgoglou, Carmelo Puliatti

For $n \geq 2$ , we consider the operator $L_{A} = - div (A (\cdot) \nabla)$ , where $A$ is a uniformly elliptic $(n + 1) \times (n + 1)$ matrix with variable coefficients, a Radon mea…

math.AP2024

A simple proof of the $1$ -dimensional flat chain conjecture

Andrea Marchese, Andrea Merlo

We give a new, elementary proof of the fact that metric 1-currents in the Euclidean space correspond to Federer-Fleming flat chains.

Marstrand's density theorem for arbitrary norms in the plane

Frobenius theorem and fine structure of tangency sets to non-involutive distributions

Layer potentials for elliptic operators with DMO-type coefficients: big pieces Tb theorem, quantitative rectifiability, and free boundary problems

A simple proof of the 1-dimensional flat chain conjecture

Layer potentials for elliptic operators with DMO-type coefficients: big pieces $T b$ theorem, quantitative rectifiability, and free boundary problems

A simple proof of the $1$ -dimensional flat chain conjecture