We present a proof of an effective uniformization for a nearly round 2-dim sphere via embedding it into the Minkowski lightcone. The method presented here makes use of the connection between the conformal geoemtry of the 2-dim sphere and the Minkowski lightcone, which reveals certain hidden equations satisfied by the conformal factor which is useful for the estimate. Comparing with the effective uniformization theorem of Klainerman and Szeftel, this method requires a stronger regularity assumption on the Gauss curvature.PDF: A proof of effective uniformization of 2-dim sphere via Minkowski lightcone.pdf
