A problem of prescribing Gaussian curvature on $S^2$
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- by Sulbha Goyal and Vinod Goyal PDF
- Proc. Amer. Math. Soc. 129 (2001), 3757-3758 Request permission
Abstract:
A class of functions $K(x)=K(x_1,x_2,x_3)$ and the corresponding solutions of \[ \Delta u + K(x)e^{2u}=1\] are obtained as a special case of the solutions of \[ \Delta ^mu+K(x)e^{au}=f(x),\qquad x=(x_1,x_2,\dots ,x_n),\] where $\Delta ^m$ is defined as $\Delta (\Delta ^{m-1})$.References
- Kuo-Shung Cheng and Joel A. Smoller, Conformal metrics with prescribed Gaussian curvature on $S^2$, Trans. Amer. Math. Soc. 336 (1993), no. 1, 219–251. MR 1087053, DOI 10.1090/S0002-9947-1993-1087053-6
- Vinod B. Goyal, Remark on a paper of Cheng and Smoller, Proc. Amer. Math. Soc. 113 (1991), no. 3, 795–797. MR 1055773, DOI 10.1090/S0002-9939-1991-1055773-9
- Jerry L. Kazdan and F. W. Warner, Curvature functions for compact $2$-manifolds, Ann. of Math. (2) 99 (1974), 14–47. MR 343205, DOI 10.2307/1971012
- J. Moser, On a nonlinear problem in differential geometry, Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971) Academic Press, New York, 1973, pp. 273–280. MR 0339258
Additional Information
- Sulbha Goyal
- Affiliation: Department of Mathematics, Tuskegee University, Tuskegee, Alabama 36088
- Vinod Goyal
- Affiliation: Department of Mathematics, Tuskegee University, Tuskegee, Alabama 36088
- Received by editor(s): December 20, 2000
- Published electronically: June 27, 2001
- Communicated by: David S. Tartakoff
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3757-3758
- MSC (2000): Primary 35J30, 35J60; Secondary 31B30
- DOI: https://doi.org/10.1090/S0002-9939-01-06330-4
- MathSciNet review: 1860514