Trading linearity for ellipticity - a novel approach to global Lorentzian geometry

Nicola Gigli (SISSA, Trieste)

May 21. 2024, 11:40 — 12:25

The concepts of Sobolev functions, elliptic operators and Banach spaces are central in modern geometric analysis. In the setting of Lorentzian geometry, however, unless one restricts the attention to Cauchy hypersurfaces these do not have a clear analogue, due to the signature of the metric tensor. Aim of the talk is to discuss some recent observations in this direction centered around the fact that for $p<1$ the $p$-D’Alambertian is elliptic on the space of time functions.

The talk is mostly based on joint project with Beran, Braun, Calisti, McCann, Ohanyan, Rott, Saemann.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Synthetic Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension (Workshop)
Lorenzo Dello Schiavo (ISTA, Klosterneuburg)
Christian Ketterer (ALU Freiburg)
Chiara Rigoni (U of Vienna)