Speaker
Vanessa Ryborz
(Universität Wien, Austria)
Description
The first order calculus on metric measure spaces by Ambrosio-Gigli-Savaré, after Cheeger turned out to be a powerful tool, for instance in the presence of curvature-dimension conditions. I study the first order calculus on smooth manifolds endowed with Riemannian metrics of low regularity and compare it to the classical first-order calculus provided by the differential structure of the manifold.
Depending on the regularity of the Riemannian metric, I will present compatibility results and provide examples where the two approaches to first order calculus are incompatible.
If time permits I will discuss applications and related results in Lorentzian signature.