THE EXISTENCE OF GENERALIZED ISOTHERMAL COORDINATES FOR HIGHER DIMENSIONAL RIEMANNIAN-MANIFOLDS

We shall show that, for any given point p on a Riemannian manifold (M, g0), there is a pointwise conformal metric g = PHI-g0 in which the g-geodesic sphere centered at p with radius r has constant mean curvature l/r for all sufficiently small r. Furthermore, the exponential map of g at p is a measure preserving map in a small ball around p.