4 citations · 13 across the 15 of their papers we have counts for
15 papers
The measure contraction property on Grushin spaces
Michael Albert, Samuël Borza
We determine the sharp measure contraction exponents of two families of Grushin-type metric measure spaces. The radial Grushin space is $\mathbb{R}^{n}\times\mat…
Ollivier-Ricci curvature for causal sets
Joe Barton, Samuël Borza, Jona Röhrig
We introduce a novel notion of Ollivier-Ricci curvature for causal sets using Lorentzian optimal transport. The construction is motivated by a new Lorentzian asymptotic formula of…
Constant mean curvature surfaces in the sub-Lorentzian Heisenberg group
Samuël Borza, Andrea Pinamonti, Omar Zoghlami
We study constant horizontal mean curvature surfaces in the sub-Lorentzian Heisenberg group. We derive the first-variation formula for horizontal area under volume-preserving radia…
Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group
Samuël Borza, Chiara Rigoni, Omar Zoghlami
We study the geodesics, Hausdorff dimension, and curvature bounds of the sub-Lorentzian Heisenberg group. Through an elementary variational approach, we provide a new proof of the…
Geodesics on Grushin spaces
Michael Albert, Samuël Borza, Maria Gordina
We consider higher-dimensional generalizations of the -Grushin plane, focusing on the problem of classification of geodesics that minimize length, also known as optimal synthesi…
Failure of the measure contraction property via quotients in higher-step sub-Riemannian structures
Samuël Borza, Luca Rizzi
We prove that the synthetic Ricci curvature lower bound known as the measure contraction property (MCP) can fail in sub-Riemannian geometry. This may happen beyond step two, if the…
Optimal transport on the sub-Lorentzian Heisenberg group
Samuël Borza, Wilhelm Klingenberg, Patrick Wood
We investigate the synthetic metric spacetime structure of the sub-Lorentzian Heisenberg group and we study the optimal transport problem in this space. The sub-Lorentzian version…
Curvature-dimension condition of sub-Riemannian -Grushin half-spaces
Samuël Borza, Kenshiro Tashiro
We provide new examples of sub-Riemannian manifolds with boundary equipped with a smooth measure that satisfy the condition. They are constructed by equipping…
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,…
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…
Measure contraction property, curvature exponent and geodesic dimension of sub-Finsler -Heisenberg groups
Samuël Borza, Kenshiro Tashiro
We initiate the study of synthetic curvature-dimension bounds in sub-Finsler geometry. More specifically, we investigate the measure contraction property , and…
Normal forms for the sub-Riemannian exponential map of , , and
Samuël Borza
The goal of this paper is to use singularity theory to find normal forms near the critical points of the sub-Riemannian exponential map. Three cases are studied: the -Grushin pl…
Local non-injectivity of the exponential map at critical points in sub-Riemannian geometry
Samuël Borza, Wilhelm Klingenberg
We prove that the sub-Riemannian exponential map is not injective in any neighbourhood of certain critical points. Namely that it does not behave like the injective map of reals gi…
Regularity and Continuity properties of the sub-Riemannian exponential map
Samuël Borza, Wilhelm Klingenberg
We prove a version of Warner's regularity and continuity properties for the sub-Riemannian exponential map. The regularity property is established by considering sub-Riemannian Jac…
Distortion coefficients of the -Grushin plane
Samuël Borza
We compute the distortion coefficients of the -Grushin plane. They are expressed in terms of generalised trigonometric functions. Estimates for the distortion coefficients are t…