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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
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…
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…