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

 

Surfaces of revolution with monotonic increasing curvature and an application to the equation $ \Delta u=1-K e^{2u}$ on $ S^{2}$


Authors: Jerry L. Kazdan and Frank W. Warner
Journal: Proc. Amer. Math. Soc. 32 (1972), 139-141
MSC: Primary 53.75; Secondary 35.00
MathSciNet review: 0290309
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Abstract: The geometric result that a compact surface of revolution in $ {R^3}$ cannot have monotonic increasing curvature is proved and applied to show that the equation $ \Delta u = 1 - K{e^{2u}}$, on $ {S^2}$, has no axially symmetric solutions u, given axially symmetric data K.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0290309-X
PII: S 0002-9939(1972)0290309-X
Article copyright: © Copyright 1972 American Mathematical Society