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Prescribing Gaussian curvature on $R^2$


Author: Sanxing Wu
Journal: Proc. Amer. Math. Soc. 125 (1997), 3119-3123
MSC (1991): Primary 58G30; Secondary 53C21
DOI: https://doi.org/10.1090/S0002-9939-97-04150-6
MathSciNet review: 1423342
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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: https://doi.org/10.1090/S0002-9939-97-04150-6
Keywords: Prescribing Gaussian curvature, semilinear elliptic PDE, integral equation
Received by editor(s): May 10, 1996
Communicated by: Peter Li
Article copyright: © Copyright 1997 American Mathematical Society

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