SUMMARY
For supersolutions of_(1.1), thus for conformal metrics on the plane of curvature ≥ 1, complex analysis does not seem to be such an appropriate tool. The theory of surfaces with integral curvature bounds in the sense of Alexandrov, turns out to be more helpful, especially, for questions concerning conformal planes of bounded total area and curvature. The above results are easy consequences of known theorems on singular metrics on S2 with bounded integral curvature and of a simple relation between conformal planes and conformal spheres, which the authors are going to explain now. While it is . . .
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