Abstract:
This thesis deals with constructions in the theory of Lorentzian (pre-)length spaces,
properties of timelike curvature bounds and rigidity statements in that context.
Lorentzian (pre-)length spaces are the Lorentzian analogue of metric and length spaces.
First, hyperbolic angles are introduced and basic properties of them are discussed.
Second, a globalization result for upper curvature bounds is given, akin to the Alexandrov
patchwork, as well as a bound on the diameter for negative lower curvature bounds,
mimicking the Bonnet-Myers theorem. Third, two rigidity results are proven for spaces
with a lower curvature bound.
Zoom-Info:
univienna.zoom.us/j/68313920244
Meeting ID: 683 1392 0244
Kenncode: 216957