Journal of Differential Geometry

The Plateau problem for marginally outer trapped surfaces

Michael Eichmair

Full-text: Open access

Abstract

We solve the Plateau problem for marginally outer trapped surfaces in general Cauchy data sets. We employ the Perron method and tools from geometric measure theory to force and control a blow-up of Jang’s equation. Substantial new geometric insights regarding the lower order properties of marginally outer trapped surfaces are gained in the process. The techniques developed in this paper are flexible and can be adapted to other non-variational existence problems.

Article information

Source
J. Differential Geom., Volume 83, Number 3 (2009), 551-584.

Dates
First available in Project Euclid: 27 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1264601035

Digital Object Identifier
doi:10.4310/jdg/1264601035

Mathematical Reviews number (MathSciNet)
MR2581357

Zentralblatt MATH identifier
1197.53075

Citation

Eichmair, Michael. The Plateau problem for marginally outer trapped surfaces. J. Differential Geom. 83 (2009), no. 3, 551--584. doi:10.4310/jdg/1264601035. https://projecteuclid.org/euclid.jdg/1264601035


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