New perspectives on the d'Alembertian from general relativity
A talk in the Bielefeld Stochastic Afternoon series by
Mathias Braun
| Abstract: | This talk has multiple objectives. First, we motivate and
review a new distributional notion of the d’Alembertian from
mathematical relativity, more precisely, a nonlinear p-version thereof,
where p is a nonzero number less than one. This operator comes from
natural Lagrangian actions introduced relatively recently. Unlike its
classical linear yet hyperbolic counterpart, it is nonlinear yet has
elliptic characteristics. Second, we describe recent comparison
estimates for the p-d’Alembertian of Lorentz distance functions
(notably a point or a spacelike hypersurface). Their new contribution
implied by prior works on optimal transport through spacetime is a
control of the timelike cut locus. Third, we illustrate exact
representation formulas for these p-d’Alembertians employing methods
from convex geometry. Fourth, several applications and open problems are
presented. Within the CRC this talk is associated to the project(s): A5, B1 |