Initial data rigidity via Dirac-Witten operators

Jonathan Glöckle (U Regensburg)

Jun 14. 2023, 15:00 — 15:50

The purpose of this talk is to derive a rigidity theorem à la Eichmayr-Galloway-Mendes (DOI:10.1007/s00220-021-04033-x) in the spin setting. The statement is concerned with initial data sets $(g,k)$ on a manifold $M$ with boundary such that $(g,k)$ satisfies the dominant energy condition as well as a condition for the null expansion scalars along the boundary. Using Dirac-Witten operators we prove that $M$ must be diffeomorphic to a cylinder $N \times [0,1]$ and is foliated by MOTS carrying non-trivial parallel spinors for the induced metrics. As a special case we also obtain a rigidity statement for Riemannian metrics of non-negative scalar curvature and with mean convex boundary.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Spectral Theory and Mathematical Relativity (Thematic Programme)
Piotr T. Chruściel (U of Vienna)
Peter Hintz (ETH Zurich)
Alexander Strohmaier (U Leeds)
Steven Morris Zelditch † (Northwestern U Evanston)