TY  - JOUR
A1  - Eichmair, Michael
A1  - Metzger, Jan
T1  - On large volume preserving stable CMC surfaces in initial data sets
JF  - Journal of differential geometry
N2  - 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.
Y1  - 2012
SN  - 0022-040X
VL  - 91
IS  - 1
SP  - 81
EP  - 102
PB  - International Press of Boston
CY  - Somerville
ER  -