What question did this study set out to answer?

The aim is to construct and analyze asymptotic foliations of lightcones using surfaces of constant spacetime mean curvature.

February 26, 2026Open Access

Foliations of asymptotically Schwarzschildean lightcones by surfaces of constant spacetime mean curvature

KKKlaus KrönckeKTH Royal Institute of Technology MWMarkus WolffKTH Royal Institute of Technology

Key Points

The aim is to construct and analyze asymptotic foliations of lightcones using surfaces of constant spacetime mean curvature.
Constructed foliations of asymptotically Schwarzschildean lightcones.
Employed geometric flow similar to Huisken-Yau's approach in Riemannian geometry.
Analyzed initial data convergence under area preserving null mean curvature flow.
Proved exponential convergence of initial data to surfaces of constant spacetime mean curvature.
Demonstrated that produced surfaces form a unique asymptotic foliation in the defined class.

Abstract

Abstract We construct asymptotic foliations of asymptotically Schwarzschildean lightcones by surfaces of constant spacetime mean curvature (STCMC). Our construction is motivated by the approach of Huisken-Yau for the Riemannian setting in employing a geometric flow. We prove that initial data within a sufficient a-priori class converges exponentially to an STCMC surface under area preserving null mean curvature flow. Further, we show that the resulting STCMC surfaces form an asymptotic foliation that is unique within the a-priori class.

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