4 papers
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…
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…
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…