17 citations · 51 across the 15 of their papers we have counts for
5 papers · 1 filter
On the converse of Pansu's Theorem
Guido De Philippis, Andrea Marchese, Andrea Merlo +2
We provide a suitable generalisation of Pansu's differentiability theorem to general Radon measures on Carnot groups and we show that if Lipschitz maps between Carnot groups are Pa…
On the density problem in the parabolic space
Andrea Merlo, Mihalis Mourgoglou, Carmelo Puliatti
In this work we extend many classical results concerning the relationship between densities, tangents and rectifiability to the parabolic spaces, namely equipped…
Physics-regularized neural network of the ideal-MHD solution operator in Wendelstein 7-X configurations
Andrea Merlo, Daniel Böckenhoff, Jonathan Schilling +3
The computational cost of constructing 3D magnetohydrodynamic (MHD) equilibria is one of the limiting factors in stellarator research and design. Although data-driven approaches ha…
On sets with unit Hausdorff density in homogeneous groups
Antoine Julia, Andrea Merlo
It is a longstanding conjecture that given a subset of a metric space, if has finite Hausdorff measure in dimension and has unit density…
On rectifiable measures in Carnot groups: Marstrand-Mattila rectifiability criterion
Gioacchino Antonelli, Andrea Merlo
In this paper we continue the study of the notion of -rectifiability in Carnot groups. We say that a Radon measure is -rectifiable, for ,…