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We prove the existence and uniqueness of the Dirichlet problem for spacelike,spherically symmetric, constant mean curvature equation with symmetric boundarydata in the extended Schwarzschild spacetime. As an application, we completelysolve the CMC foliation conjecture which is posted by Malec and O Murchadha in2003.

Dirichlet problem for the constant mean curvature equation and CMC foliation in the extended Schwarzschild spacetime