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.
- Pub Date:
- November 2007
- Mathematics - Differential Geometry
- To app. in J. Differential Geometry. New title, introduction rewritten with motivation and several concise references to the literature added. Former Section 3 and Appendix B are now subsumed in Section 2. Remark 3.2 and Lemma A.1 added. Sections 3 and 4 now include a well-known geometric argument driving Serrin's classical construction of boundary barriers