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

Abstract

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.

22 pages, 7 figures

References in corpus (2)

• The general spherically symmetric constant mean curvature foliations of the Schwarzschild solution
• Spacelike spherically symmetric CMC foliation in the extended Schwarzschild spacetime

Cited by in corpus (2)

• Spherically symmetric solutions of the $\lambda$-R model
• Existence of constant mean curvature foliation in the extended Schwarzschild spacetime