Herman Weyl in 1916 described the Schwarzschild metric
by a single harmonic function with a pole.  Since then, the Einstein
equation with time symmetry can be regarded as an elliptic variational
problem, and I will report on the recent progress in this direction,
including a series of collaborative work with Gilbert Weinstein and Marcus
Khuri.  We will introduce spactimes of dimension four and five with some
rotational symmetries, and discuss the difference in 4 and 5, and some new
geometric consequences..