Mattia Magnabosco

activity

20212026

most citedOptimal maps and local-to-global property in negative dimensional spaces with Ricci curvature bounded from below

4 citations · 12 across the 16 of their papers we have counts for

collaborators

19 papers

math.DG2026

New Topological Restrictions For Spaces With Nonnegative Ricci Curvature

Alessandro Cucinotta, Mattia Magnabosco, Daniele Semola

We obtain new topological restrictions for complete Riemannian manifolds with nonnegative Ricci curvature and RCD(0,n) spaces. Our main results are a Betti number rigidity theorem…

math.MG2025

On the rectifiability of $CD (K, N)$ and $MCP (K, N)$ spaces with unique tangents

Mattia Magnabosco, Andrea Mondino, Tommaso Rossi

We prove rectifiability results for $CD (K, N)$ and $MCP (K, N)$ metric measure spaces $(X, d, m)$ with pointwise Ahlfors regular reference…

math.DG2025

On perimeter minimizing sets in manifolds with quadratic volume growth

Alessandro Cucinotta, Mattia Magnabosco

This paper studies whether the presence of a perimeter minimizing set in a Riemannian manifold $(M, g)$ forces an isometric splitting. We show that this is the case when $M$ has non…

math.FA2024

Gradient flows of $(K, N)$ -convex functions with negative $N$

Lorenzo Dello Schiavo, Mattia Magnabosco, Chiara Rigoni

We discuss $(K, N)$ -convexity and gradient flows for $(K, N)$ -convex functionals on metric spaces, in the case of real $K$ and negative $N$ . In this generality, it is necessary to co…

math.MG2024

On the existence of $L^{p}$ -Optimal Transport maps for norms on $R^{N}$

Guoxi Liu, Mattia Magnabosco, Yicheng Xia

In this paper, we prove existence of $L^{p}$ -optimal transport maps with $p \in (1, \infty)$ in a class of branching metric spaces defined on $R^{N}$ . In particular, we introdu…

math.MG2024

Metric conditions that guarantee existence and uniqueness of Optimal Transport maps

Shucheng Li, Mattia Magnabosco, Timo Schultz

We investigate metric conditions that allow to prove existence and uniqueness of a map solving the Monge problem between two marginals in a metric (measure) space, proving two main…

math.MG2024★ 2 cited

Curvature exponent of sub-Finsler Heisenberg groups

Samuël Borza, Mattia Magnabosco, Tommaso Rossi +1

The curvature exponent $N_{curv}$ of a metric measure space is the smallest number $N$ for which the measure contraction property $MCP (0, N)$ holds. In this paper,…

math.DG2024

A review of the tangent space in sub-Finsler geometry and applications to the failure of the $CD$ 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…

math.MG2024★ 2 cited

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…

math.MG2023

Examples of $C D (0, N)$ spaces with non-constant dimension

Mattia Magnabosco

In this work, we generalize the results obtained in (J. Geom. Anal., 32(6):Paper No.173, 32, 2022), presenting some examples of $C D (0, N)$ spaces having different dimensions in diff…

math.MG2023

Failure of the curvature-dimension condition in sub-Finsler manifolds

Mattia Magnabosco, Tommaso Rossi

The Lott-Sturm-Villani curvature-dimension condition $CD (K, N)$ provides a synthetic notion for a metric measure space to have curvature bounded from below by $K$ and dimen…

math.MG2022

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,…

math.DG2022

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…

math.MG2022

A canonical infinitesimally Hilbertian structure on locally Minkowski spaces

Mattia Magnabosco, Chiara Rigoni

The aim of this paper is to show the existence of a canonical distance $d^{'}$ defined on a locally Minkowski metric measure space $(X, d, m)$ such tha…

math.DG2022★ 1 cited

Almost-Riemannian manifolds do not satisfy the $CD$ condition

Mattia Magnabosco, Tommaso Rossi

The Lott-Sturm-Villani curvature-dimension condition $CD (K, N)$ provides a synthetic notion for a metric-measure space to have curvature bounded from below by $K$ and dimen…

math.DG2021★ 4 cited

Optimal maps and local-to-global property in negative dimensional spaces with Ricci curvature bounded from below

Mattia Magnabosco, Chiara Rigoni

In this paper we investigate two important properties of metric measure spaces satisfying the reduced curvature-dimension condition for negative values of the dimension parameter:…

math.MG2021★ 3 cited

Convergence of metric measure spaces satisfying the CD condition for negative values of the dimension parameter

Mattia Magnabosco, Chiara Rigoni, Gerardo Sosa

We study the problem of whether the curvature-dimension condition with negative values of the generalized dimension parameter is stable under a suitable notion of convergence. To t…

math.MG2021

A Metric Stability Result for the Very Strict CD Condition

Mattia Magnabosco

In (Calc.Var.PDE 2018) Schultz generalized the work of Rajala and Sturm (Calc.Var.PDE 2014), proving that a weak non-branching condition holds in the more general setting of very s…

math.MG2021

Example of an Highly Branching CD Space

Mattia Magnabosco

Ketterer and Rajala showed an example of metric measure space, satisfying the measure contraction property $M C P (0, 3)$ , that has different topological dimensions at different region…

New Topological Restrictions For Spaces With Nonnegative Ricci Curvature

On the rectifiability of CD(K,N) and MCP(K,N) spaces with unique tangents

On perimeter minimizing sets in manifolds with quadratic volume growth

Gradient flows of (K,N)-convex functions with negative N

On the existence of Lp-Optimal Transport maps for norms on RN

Metric conditions that guarantee existence and uniqueness of Optimal Transport maps

Curvature exponent of sub-Finsler Heisenberg groups

A review of the tangent space in sub-Finsler geometry and applications to the failure of the CD condition

Measure contraction property and curvature-dimension condition on sub-Finsler Heisenberg groups

Examples of CD(0,N) spaces with non-constant dimension

Failure of the curvature-dimension condition in sub-Finsler manifolds

The strong Brunn--Minkowski inequality and its equivalence with the CD condition

The Brunn--Minkowski inequality implies the CD condition in weighted Riemannian manifolds

A canonical infinitesimally Hilbertian structure on locally Minkowski spaces

Almost-Riemannian manifolds do not satisfy the CD condition

Optimal maps and local-to-global property in negative dimensional spaces with Ricci curvature bounded from below

Convergence of metric measure spaces satisfying the CD condition for negative values of the dimension parameter

A Metric Stability Result for the Very Strict CD Condition

Example of an Highly Branching CD Space

On the rectifiability of $CD (K, N)$ and $MCP (K, N)$ spaces with unique tangents

Gradient flows of $(K, N)$ -convex functions with negative $N$

On the existence of $L^{p}$ -Optimal Transport maps for norms on $R^{N}$

A review of the tangent space in sub-Finsler geometry and applications to the failure of the $CD$ condition

Examples of $C D (0, N)$ spaces with non-constant dimension

Almost-Riemannian manifolds do not satisfy the $CD$ condition