32 citations · 130 across the 34 of their papers we have counts for
4 papers · 1 filter
Nonexistence of isoperimetric sets in spaces of positive curvature
Gioacchino Antonelli, Federico Glaudo
For every , we construct a noncompact smooth -dimensional Riemannian manifold with strictly positive sectional curvature without isoperimetric sets for any volume below…
Topological regularity of isoperimetric sets in PI spaces having a deformation property
Gioacchino Antonelli, Enrico Pasqualetto, Marco Pozzetta +1
We prove topological regularity results for isoperimetric sets in PI spaces having a suitable deformation property, which prescribes a control on the increment of the perimeter of…
Isoperimetric problem and structure at infinity on Alexandrov spaces with nonnegative curvature
Gioacchino Antonelli, Marco Pozzetta
In this paper we consider nonnegatively curved finite dimensional Alexandrov spaces with a non-collapsing condition, i.e., such that unit balls have volumes uniformly bounded from…
Carnot rectifiability and Alberti representations
Gioacchino Antonelli, Enrico Le Donne, Andrea Merlo
A metric measure space is said to be Carnot-rectifiable if it can be covered up to a null set by countably many biLipschitz images of compact sets of a fixed Carnot group. In this…