Mean curvature flow of spacelike hypersurfaces near null initial data

Klaus Ecker

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17 Citations (Scopus)


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
Issue number2
Publication statusPublished - 2003

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