Journal of Differential Geometry

On the evolution of hypersurfaces by their inverse null mean curvature

Kristen Moore

Full-text: Open access

Abstract

We introduce a new geometric evolution equation for hypersurfaces in asymptotically flat spacetime initial data sets, that unites the theory of marginally outer trapped surfaces (MOTS) with the study of inverse mean curvature flow. A theory of weak solutions is developed using level-set methods and an appropriate variational principle. This new flow has a natural application as a variational-type approach to constructing MOTS, and this work also gives new insights into the theory of weak solutions of the inverse mean curvature flow.

Article information

Source
J. Differential Geom., Volume 98, Number 3 (2014), 425-466.

Dates
First available in Project Euclid: 28 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1406552277

Digital Object Identifier
doi:10.4310/jdg/1406552277

Mathematical Reviews number (MathSciNet)
MR3263523

Zentralblatt MATH identifier
1305.33006

Citation

Moore, Kristen. On the evolution of hypersurfaces by their inverse null mean curvature. J. Differential Geom. 98 (2014), no. 3, 425--466. doi:10.4310/jdg/1406552277. https://projecteuclid.org/euclid.jdg/1406552277


Export citation