@article{EichmairMetzger2012,
  author    = {Eichmair, Michael and Metzger, Jan},
  title     = {On large volume preserving stable CMC surfaces in initial data sets},
  series = {Journal of differential geometry},
  volume    = {91},
  journal   = {Journal of differential geometry},
  number    = {1},
  publisher = {International Press of Boston},
  address   = {Somerville},
  issn      = {0022-040X},
  pages     = {81 -- 102},
  year      = {2012},
  abstract  = {Let (M, g) be a complete 3-dimensional asymptotically flat manifold with everywhere positive scalar curvature. We prove that, given a compact subset K subset of M, all volume preserving stable constant mean curvature surfaces of sufficiently large area will avoid K. This complements the results of G. Huisken and S.-T. Yau [17] and of J. Qing and G. Tian [26] on the uniqueness of large volume preserving stable constant mean curvature spheres in initial data sets that are asymptotically close to Schwarzschild with mass m > 0. The analysis in [17] and [26] takes place in the asymptotic regime of M. Here we adapt ideas from the minimal surface proof of the positive mass theorem [32] by R. Schoen and S.-T. Yau and develop geometric properties of volume preserving stable constant mean curvature surfaces to handle surfaces that run through the part of M that is far from Euclidean.},
  language  = {en}
}