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The equation for Gaussian curvature of a conformal metric is a special case of the classical differential equation. δu = f(u) for u ∈C2(ω), where ω⊂R2. We will use a technique introduced by Carleman to find restrictions on f and the set where a subharmonic function u can satisfy the above equation. This result will generate a relationship between the curvature and the metric of a nonpositively curved surface.