10 citations · 17 across the 10 of their papers we have counts for
13 papers
Tubes in sub-Riemannian geometry and a Weyl's invariance result for curves in the Heisenberg groups
Tania Bossio, Luca Rizzi, Tommaso Rossi
The purpose of the paper is threefold: first, we prove optimal regularity results for the distance from submanifolds of general rank-varying sub-Riemannian structures. Then,…
Curvature exponent of sub-Finsler Heisenberg groups
Samuël Borza, Mattia Magnabosco, Tommaso Rossi +1
The curvature exponent of a metric measure space is the smallest number for which the measure contraction property holds. In this paper,…
A review of the tangent space in sub-Finsler geometry and applications to the failure of the condition
Mattia Magnabosco, Tommaso Rossi
We review the construction of the tangent space to a sub-Finsler manifold in the measured Gromov-Hausdorff sense. Under suitable assumptions on the measure, the metric measure tang…
Measure contraction property and curvature-dimension condition on sub-Finsler Heisenberg groups
Samuël Borza, Mattia Magnabosco, Tommaso Rossi +1
In this paper, we investigate the validity of synthetic curvature-dimension bounds in the sub-Finsler Heisenberg group, equipped with a positive smooth measure. Firstly, we study t…
Failure of the curvature-dimension condition in sub-Finsler manifolds
Mattia Magnabosco, Tommaso Rossi
The Lott-Sturm-Villani curvature-dimension condition provides a synthetic notion for a metric measure space to have curvature bounded from below by and dimen…
First-order heat content asymptotics on spaces
Emanuele Caputo, Tommaso Rossi
In this paper, we prove first-order asymptotics on a bounded open set of the heat content when the ambient space is an space, under a regularity condition for the…
The strong Brunn--Minkowski inequality and its equivalence with the CD condition
Mattia Magnabosco, Lorenzo Portinale, Tommaso Rossi
In the setting of essentially non-branching metric measure spaces, we prove the equivalence between the curvature dimension condition CD(K,N), in the sense of Lott--Sturm--Villani,…
The Brunn--Minkowski inequality implies the CD condition in weighted Riemannian manifolds
Mattia Magnabosco, Lorenzo Portinale, Tommaso Rossi
The curvature dimension condition CD(K,N), pioneered by Sturm and Lott--Villani, is a synthetic notion of having curvature bounded below and dimension bounded above, in the non-smo…
The relative heat content for submanifolds in sub-Riemannian geometry
Tommaso Rossi
We study the small-time asymptotics of the relative heat content for submanifolds in sub-Riemannian geometry. First, we prove the existence of a smooth tubular neighborhood for sub…
Almost-Riemannian manifolds do not satisfy the condition
Mattia Magnabosco, Tommaso Rossi
The Lott-Sturm-Villani curvature-dimension condition provides a synthetic notion for a metric-measure space to have curvature bounded from below by and dimen…
Relative heat content asymptotics for sub-Riemannian manifolds
Andrei Agrachev, Luca Rizzi, Tommaso Rossi
The relative heat content associated with a subset of a sub-Riemannian manifold, is defined as the total amount of heat contained in at time , with uniform init…
Integrability of the sub-Riemannian mean curvature at degenerate characteristic points in the Heisenberg group
Tommaso Rossi
We address the problem of integrability of the sub-Riemannian mean curvature of an embedded hypersurface around isolated characteristic points. The main contribution of this note i…
Heat content asymptotics for sub-Riemannian manifolds
Luca Rizzi, Tommaso Rossi
We study the small-time asymptotics of the heat content of smooth non-characteristic domains of a general rank-varying sub-Riemannian structure, equipped with an arbitrary smooth m…