4 papers
Null distance on cosmological spacetimes and monotone convergence
Miguel Prados-Abad, Omar Zoghlami
The metric theory of spacetimes studies Lorentzian manifolds using tools of metric geometry. This is achieved via the null distance, which is a definite distance constructed from a…
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…
Conformal transformations of metric spaces and Lorentzian pre-length spaces
Miguel Manzano, Karim Mosani, Clemens Sämann +1
We introduce conformal transformations in the synthetic setting of metric spaces and Lorentzian (pre-)length spaces. Our main focus lies on the Lorentzian case, where, motivated by…
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…