32 citations · 130 across the 34 of their papers we have counts for
7 papers · 1 filter
A sharp spectral splitting theorem
Gioacchino Antonelli, Marco Pozzetta, Kai Xu
We prove a sharp spectral generalization of the Cheeger--Gromoll splitting theorem. We show that if a complete non-compact Riemannian manifold of dimension has at lea…
Vertical curves and vertical fibers in the Heisenberg group
Gioacchino Antonelli, Robert Young
Let denote the three-dimensional Heisenberg group. In this paper, we study vertical curves in and fibers of maps from a metr…
Sharp defective log-Sobolev inequalities on H-type groups
Gioacchino Antonelli, Mattia Calzi, Maria Gordina
In this paper we prove a sharp defective log-Sobolev inequality on H-type groups. Then we use such an inequality to show exponential integrability of Lipschitz functions with respe…
Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature
Gioacchino Antonelli, Marco Pozzetta, Daniele Semola
Let be a complete Riemannian manifold which is not isometric to , has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature…
Ergodic maps and the cohomology of nilpotent Lie groups
Gioacchino Antonelli, Robert Young
In this paper, we study how the cohomology of nilpotent groups is affected by Lipschitz maps. We show that, given a smooth Lipschitz map between two simply-connected nilpotent…
New spectral Bishop-Gromov and Bonnet-Myers theorems and applications to isoperimetry
Gioacchino Antonelli, Kai Xu
We show a sharp and rigid spectral generalization of the classical Bishop--Gromov volume comparison theorem: if a closed Riemannian manifold of dimension satisfies…