@article{EichmairMetzger2016,
  author    = {Eichmair, Michael and Metzger, Jan},
  title     = {JENKINS-SERRIN-TYPE RESULTS FOR THE JANG EQUATION},
  series = {Journal of differential geometry},
  volume    = {102},
  journal   = {Journal of differential geometry},
  publisher = {International Press of Boston},
  address   = {Somerville},
  issn      = {0022-040X},
  doi       = {10.4310/jdg/1453910454},
  pages     = {207 -- 242},
  year      = {2016},
  abstract  = {Let (M, g, k) be an initial data set for the Einstein equations of general relativity. We show that a canonical solution of the Jang equation exists in the complement of the union of all weakly future outer trapped regions in the initial data set with respect to a given end, provided that this complement contains no weakly past outer trapped regions. The graph of this solution relates the area of the horizon to the global geometry of the initial data set in a non-trivial way. We prove the existence of a Scherk-type solution of the Jang equation outside the union of all weakly future or past outer trapped regions in the initial data set. This result is a natural exterior analogue for the Jang equation of the classical Jenkins Serrin theory. We extend and complement existence theorems [19, 20, 40, 29, 18, 31, 11] for Scherk-type constant mean curvature graphs over polygonal domains in (M, g), where (M, g) is a complete Riemannian surface. We can dispense with the a priori assumptions that a sub solution exists and that (M, g) has particular symmetries. Also, our method generalizes to higher dimensions.},
  language  = {en}
}