Non-constant mean curvature trumpet solutions for the Einstein constraint equations

Abstract

We prove the existence of a large class of initial data for the vacuum Einstein equations which possess a finite number of asymptotically Euclidean and asymptotically conformally cylindrical or periodic ends. Aside from being asymptotically constant, only mild conditions on the mean curvature of these initial data sets are imposed.

References in corpus (4)

• The Conformal Method and the Conformal Thin-Sandwich Method Are the Same
• A new point of view on the solutions to the Einstein constraint equations with arbitrary mean curvature and small TT-tensor
• The Yamabe invariant for axially symmetric two Kerr black holes initial data
• A far-from-CMC existence result for the constraint equations on manifolds with ends of cylindrical type