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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A problem of prescribing Gaussian curvature on $S^2$


Authors: Sulbha Goyal and Vinod Goyal
Journal: Proc. Amer. Math. Soc. 129 (2001), 3757-3758
MSC (2000): Primary 35J30, 35J60; Secondary 31B30
Published electronically: June 27, 2001
MathSciNet review: 1860514
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Abstract | References | Similar Articles | Additional Information

Abstract:

A class of functions $K(x)=K(x_1,x_2,x_3)$ and the corresponding solutions of

\begin{displaymath}\Delta u + K(x)e^{2u}=1\end{displaymath}

are obtained as a special case of the solutions of

\begin{displaymath}\Delta^mu+K(x)e^{au}=f(x),\qquad x=(x_1,x_2,\dots,x_n),\end{displaymath}

where $\Delta^m$ is defined as $\Delta(\Delta^{m-1})$.


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Additional Information

Sulbha Goyal
Affiliation: Department of Mathematics, Tuskegee University, Tuskegee, Alabama 36088

Vinod Goyal
Affiliation: Department of Mathematics, Tuskegee University, Tuskegee, Alabama 36088

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06330-4
PII: S 0002-9939(01)06330-4
Keywords: Laplace operator, Gaussian curvature, conformally equivalent, metric
Received by editor(s): December 20, 2000
Published electronically: June 27, 2001
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2001 American Mathematical Society