A new Geometry for Einstein’s Theory of Relativity & Beyond

Publications

  • The equivalence of isocapacitary notions of mass

  • A Closeness Function on Coarse Grained Lorentzian Geometries

  • Timelike conjugate points in Lorentzian length spaces

  • Quantitative isoperimetric inequalities in capillarity problems and cones in strong and barycentric forms

  • Continuity of critical points for 1-dimensional non-local energies

  • Curvature-dimension condition of sub-Riemannian α-Grushin half-spaces

  • The Penrose singularity theorem, MOTS stability, and horizon topology in weighted spacetimes

  • Concavity of spacetimes

  • Topological cones and positively polarizable hyperbolic norms

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

  • Reshetnyak Majorisation and discrete upper curvature bounds for Lorentzian length spaces

  • The failure of the Ehlers–Kundt conjecture in the impulsive case

  • Rigidity aspects of a cosmological singularity theorem

  • Geodesics on Grushin spaces

  • Generalizing the Penrose cut-and-paste method: Null shells with pressure and energy flux

  • Null Distance and Temporal Functions

  • Spacetime reconstruction by order and number

  • Gromov’s reconstruction theorem and measured Gromov-Hausdorff convergence in Lorentzian geometry

  • Generalized cones admitting a curvature-dimension condition

  • A synthetic Lorentzian Cartan-Hadamard theorem

  • Particle approximation of nonlocal interaction energies

  • Gradient flows of \((K,N)\)-convex functions with negative \(N\)

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

  • Geodesic causality in Kerr spacetimes with \(\vert a\vert\ge M\)

  • Optimal transport on the sub-Lorentzian Heisenberg group

  • Distributional sectional curvature bounds for Riemannian metrics of low regularity

  • Quantum Geometry of the Light Cone: Fock representation and Spectrum of Radiated Power

  • On the Hauptvermutung of Causal Set Theory

  • Hawking’s singularity theorem for Lipschitz Lorentzian metrics

  • Splitting theorems for weighted Finsler spacetimes via the \(p\)-d’Alembertian: beyond the Berwald case

  • An elliptic proof of the splitting theorems from Lorentzian geometry

  • A nonlinear d’Alembert comparison theorem and causal differential calculus on metric measure spacetimes

  • Marginally outer trapped tubes in de Sitter spacetime

  • Ricci curvature bounds and rigidity for non-smooth Riemannian and semi-Riemannian metrics