Prescribing Gaussian curvature on 𝑅²

Wu, Sanxing

doi:10.1090/S0002-9939-97-04150-6

Prescribing Gaussian curvature on $R^2$
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Proc. Amer. Math. Soc. 125 (1997), 3119-3123 Request permission

Abstract:

We derive a sufficient condition for a radially symmetric function $K(x)$ which is positive somewhere to be a conformal curvature on $R^2$. In particular, we show that every nonnegative radially symmetric continuous function $K(x)$ on $R^2$ is a conformal curvature.

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