  This work presents uniform preconditioners for the discrete Laplace--Beltrami
operator on hypersurfaces. In particular, within the framework of fast
auxiliary space preconditioning (FASP), we develop efficient and user-friendly
multilevel preconditioners for the Laplace--Beltrami type equation discretized
by Lagrange, nonconforming linear, and discontinuous Galerkin elements. The
analysis applies to semi-definite problems on a closed surface. Numerical
experiments on 2d surfaces and 3d hypersurfaces are presented to illustrate the
efficiency of the proposed preconditioners.
