Band width estimates of CMC initial data sets

TL;DR

This paper extends Gromov's band width estimate to constant mean curvature initial data sets, providing three independent proofs using different mathematical techniques.

Contribution

It introduces a generalized band width estimate for CMC initial data sets with three novel proof methods.

Findings

Established a generalized band width estimate for CMC initial data sets.

Provided three independent proofs using hypersurface stability, spacetime harmonic functions, and Dirac operators.

Enhanced understanding of geometric constraints in general relativity.

Abstract

We generalize a band width estimate of Gromov to CMC initial data sets. We give three independent proofs: via the stability of a hypersurface with prescribed null expansion, via a perturbation of the spacetime harmonic function and via the Dirac operator.