Conformal Metrics in R^2 with Prescribed Gaussian Curvature and Positive Total Curvature Robert McOwen Indiana University Mathematics Journal 1985 text pdf 10.1512/iumj.1985.34.34005 10.1512/iumj.1985.34.34005 en Indiana Univ. Math. J. 34 (1985) 97 - 104 state-of-the-art mathematics http://iumj.org/access/