3 papers
math-ph2026
Monge-Ampere Geometry and Vortices
Lewis Napper, Ian Roulstone, Vladimir Rubtsov +1
We introduce a new approach to Monge-Ampere geometry based on techniques from higher symplectic geometry. Our work is motivated by the application of Monge-Ampere geometry to the P…
math.DG2025
Alexandrov's Patchwork and the Bonnet--Myers Theorem for Lorentzian length spaces
Tobias Beran, Lewis Napper, Felix Rott
We present several key results for Lorentzian pre-length spaces with global timelike curvature bounds. Most significantly, we construct a Lorentzian analogue to Alexandrov's Patchw…
math.DG2025
A Toponogov globalisation result for Lorentzian length spaces
Tobias Beran, John Harvey, Lewis Napper +1
In the synthetic geometric setting introduced by Kunzinger and Sämann, we present an analogue of Toponogov's Globalisation Theorem which applies to Lorentzian length spaces with l…