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arXiv · 2412.17563

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

Klaus Kroencke·Markus Wolff
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Abstract

We construct asymptotic foliations of asymtotically 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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Klaus Kroencke, Markus Wolff. 2024-12-23. Foliations of asymptotically Schwarzschildean lightcones by surfaces of constant spacetime mean curvature. https://arxiv.org/abs/2412.17563

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