TY - JOUR
T1 - Large Isoperimetric Regions in Asymptotically Hyperbolic Manifolds
AU - Chodosh, Otis
N1 - Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - We show the existence of isoperimetric regions of sufficiently large volumes in general asymptotically hyperbolic three manifolds. Furthermore, we show that large coordinate spheres are uniquely isoperimetric in manifolds that are Schwarzschild–anti-deSitter at infinity. These results have important repercussions for our understanding of spacelike hypersurfaces in Lorentzian space-times which are asymptotic to null infinity. In fact, as an application of our results, we verify the asymptotically hyperbolic Penrose inequality in the special case of the existence of connected isoperimetric regions of all volumes.
AB - We show the existence of isoperimetric regions of sufficiently large volumes in general asymptotically hyperbolic three manifolds. Furthermore, we show that large coordinate spheres are uniquely isoperimetric in manifolds that are Schwarzschild–anti-deSitter at infinity. These results have important repercussions for our understanding of spacelike hypersurfaces in Lorentzian space-times which are asymptotic to null infinity. In fact, as an application of our results, we verify the asymptotically hyperbolic Penrose inequality in the special case of the existence of connected isoperimetric regions of all volumes.
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U2 - 10.1007/s00220-015-2457-y
DO - 10.1007/s00220-015-2457-y
M3 - Article
AN - SCOPUS:84944598033
SN - 0010-3616
VL - 343
SP - 393
EP - 443
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -