32 citations · 130 across the 34 of their papers we have counts for
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Lipschitz Carnot-Carathéodory structures and their limits
Gioacchino Antonelli, Enrico Le Donne, Sebastiano Nicolussi Golo
In this paper we discuss the convergence of distances associated to converging structures of Lipschitz vector fields and continuously varying norms on a smooth manifold. We prove t…
On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth
Gioacchino Antonelli, Elia Bruè, Mattia Fogagnolo +1
In this paper we provide new existence results for isoperimetric sets of large volume in Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth. We find…
Isoperimetric sets in spaces with lower bounds on the Ricci curvature
Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta
In this paper we study regularity and topological properties of volume constrained minimizers of quasi-perimeters in spaces where the reference measure is the Hausdorff m…
Unextendable intrinsic Lipschitz curves
Gioacchino Antonelli, Andrea Merlo
In the setting of Carnot groups, we exhibit examples of intrinisc Lipschitz curves of positive -measure that intersect every connected intrinsic Lipschitz curve in a…
On rectifiable measures in Carnot groups: representation
Gioacchino Antonelli, Andrea Merlo
This paper deals with the theory of rectifiability in arbitrary Carnot groups, and in particular with the study of the notion of -rectifiable measure. First, we show t…
The isoperimetric problem on Riemannian manifolds via Gromov-Hausdorff asymptotic analysis
Gioacchino Antonelli, Mattia Fogagnolo, Marco Pozzetta
In this paper we prove the existence of isoperimetric regions of any volume in Riemannian manifolds with Ricci bounded below assuming Gromov--Hausdorff asymptoticity to the suitabl…