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Prescribing Gaussian curvature on $R^2$

Author(s): Sanxing Wu
Journal: Proc. Amer. Math. Soc. 125 (1997), 3119-3123.
MSC (1991): Primary 58G30; Secondary 53C21
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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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Additional Information:

Sanxing Wu
Affiliation: Department of Applied Mathematics, 100083, Beijing University of Aeronautics and Astronautics, Beijing, People's Republic of China

DOI: 10.1090/S0002-9939-97-04150-6
PII: S 0002-9939(97)04150-6
Keywords: Prescribing Gaussian curvature, semilinear elliptic PDE, integral equation
Received by editor(s): May 10, 1996
Communicated by: Peter Li
Copyright of article: Copyright 1997, American Mathematical Society

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