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

Understand

We prove the existence and uniqueness of the Dirichlet problem for spacelike, spherically symmetric, constant mean curvature equation with symmetric boundary data in the extended Schwarzschild spacetime.

• As an application, we completely solve the CMC foliation conjecture which is posted by Malec and O Murchadha in 2003.