On the long neck principle and width estimates for initial data sets

Abstract

In this paper, we prove the long neck principle, band width estimates, and width inequalities of the geodesic collar neighborhoods of the boundary in the setting of general initial data sets for the Einstein equations, subject to certain energy conditions corresponding to the lower bounds of scalar curvature on Riemannian manifolds. Our results are established via the spinorial Callias operator approach.

to appear in the Mathematische Zeitschrift