  We present a proof of an effective uniformization for a nearly round 2-dim
sphere. The method presented here makes use of the connection between the
conformal geometry of the 2-dim sphere and the Minkowski lightcone, which
reveals certain hidden equations satisfied by the conformal factor. Comparing
with the effective uniformization theorem of Klainerman and Szeftel, this
method requires a stronger regularity assumption on the Gauss curvature. We
also discuss the stability of the effective uniformization of Klainerman and
Szeftel. The proof is simplified with the help of a geometric observation that
an isometric embedding of a round sphere into the Euclidean space can be
obtained by taking an orthogonal basis of the first eigenspace of the Laplacian
operator as the rectangular coordinates.
