L. V. Ahlfors, An extension of Schwartz's lemma, Trans. Amer. Math. Soc, vol.43, pp.359-364, 1938.

K. Cheng and C. Lin, Conformal metrics with prescribed nonpositive Gaussian on R 2, Calc. Var. PDE, vol.11, pp.203-231, 2000.

K. Cheng and W. Ni, On the structure of the conformal Gaussian curvature equation on R 2, Duke Math. J, vol.62, pp.721-737, 1991.

K. Cheng and W. Ni, On the structure of the conformal Gaussian curvature equation on R 2 II, Math. Ann, vol.290, pp.671-680, 1991.

J. Kazdan and F. Warner, Curvature functions for open 2-manifolds, Ann. Math, vol.99, pp.203-219, 1974.

R. Mcowen, On the equation ?u + Ke 2u = f and prescribed negative curvature in R 2, J. Math. Anal. Appl, vol.103, pp.365-370, 1984.

R. Mcowen, Conformal metrics in R 2 with prescribed Gaussian curvature and positive total curvature, Indiana Univ. Math. J, vol.34, pp.97-104, 1985.

W. Ni, On the elliptic equation ?u + K(x)e 2u = 0 and conformal metric with prescribed Gaussian curvatures, Invent. Math, vol.66, pp.343-352, 1982.

D. Sattinger, Conformal metrics in R 2 with prescribed curvature, Indiana Univ. Math. J, vol.22, pp.1-4, 1972.