Samuël Borza

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math.DG2025

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…

math.DG2025

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…

math.DG2023

Normal forms for the sub-Riemannian exponential map of $G_{α}$ , $SU (2)$ , and $SL (2)$

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 $α$ -Grushin pl…

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group

Failure of the measure contraction property via quotients in higher-step sub-Riemannian structures

Normal forms for the sub-Riemannian exponential map of Gα​, SU(2), and SL(2)

Normal forms for the sub-Riemannian exponential map of $G_{α}$ , $SU (2)$ , and $SL (2)$