Mean curvature flow of spacelike hypersurfaces near null initial data

Klaus Ecker

Research output: Contribution to journalArticleResearchpeer-review

17 Citations (Scopus)

Abstract

We prove an interior estimate for the gradient function of space-like hypersurfaces which move by mean curvature in a Lorentzian manifold. This estimate depends only on a time fraction which measures how far the hypersurfaces are from being null. As a consequence, we show that under mean curvature flow a weakly spacelike initial hypersurface instantaneously becomes smooth and strictly spacelike except along null geodesics which extend to its boundary.
Original languageEnglish
Pages (from-to)181 - 205
Number of pages25
JournalCommunications in Analysis and Geometry
Volume11
Issue number2
Publication statusPublished - 2003

Cite this