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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Scalar curvatures on $ S\sp 2$


Authors: Wen Xiong Chen and Wei Yue Ding
Journal: Trans. Amer. Math. Soc. 303 (1987), 365-382
MSC: Primary 35J60; Secondary 49A40, 53C20, 58G30
DOI: https://doi.org/10.1090/S0002-9947-1987-0896027-4
MathSciNet review: 896027
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Abstract: A theorem for the existence of solutions of the nonlinear elliptic equation $ - \Delta u + 2 = R(x){e^u},\;x \in {S^2}$, is proved by using a "mass center" analysis technique and by applying a continuous "flow" in $ {H^1}({S^2})$ controlled by $ \nabla R$.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0896027-4
Article copyright: © Copyright 1987 American Mathematical Society