Remark on “A problem of prescribing Gaussian curvature on $S^2$" [\text{Proc. Amer. Math. Soc. 129 (2001), no. 12, 3757–3758}]
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- by Edward M. Fan PDF
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Abstract:
In this note, we remark on a 2001 paper of S. Goyal and V. Goyal. The main result of this work is that they used some elementary method to find a class of functions $K(x)=K(x_1,x_2,x_3)$ for which the solutions to \[ \Delta u + K(x)e^{2u} = 1\] on $S^2$ can be obtained. We observe that this class of functions that they studied is actually the trivial one, i.e. the class of positive constant functions.References
- Sulbha Goyal and Vinod Goyal, A problem of prescribing Gaussian curvature on $S^2$, Proc. Amer. Math. Soc. 129 (2001), no. 12, 3757–3758. MR 1860514, DOI 10.1090/S0002-9939-01-06330-4
Additional Information
- Edward M. Fan
- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
- Email: efan@math.princeton.edu
- Received by editor(s): July 18, 2005
- Published electronically: June 13, 2006
- Additional Notes: This work was partially supported by NSF Graduate Research Fellowship
- Communicated by: David S. Tartakoff
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 107-108
- MSC (2000): Primary 35J60; Secondary 31B30, 35J30, 53C21
- DOI: https://doi.org/10.1090/S0002-9939-06-08461-9
- MathSciNet review: 1860514