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Solvability of the equation $ \Delta\sb gu+\tilde{S}u\sp \sigma=Su$ on manifolds


Author: Jun Jie Tang
Journal: Proc. Amer. Math. Soc. 121 (1994), 83-92
MSC: Primary 53C21; Secondary 35J60, 53C25, 58G30
DOI: https://doi.org/10.1090/S0002-9939-1994-1174496-1
MathSciNet review: 1174496
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Abstract: For the negative Yamabe invariant and $ \tilde S \leq 0$, we obtain that the equation $ {\Delta _g}u + \tilde S{u^\sigma } = Su$ has a positive solution if and only if the supremum of the Yamabe invariant over all smooth coverings of the 0-level set of $ \tilde S$ is positive.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1174496-1
Keywords: Yamabe invariant, first eigenvalue, 0-level set, smooth covering
Article copyright: © Copyright 1994 American Mathematical Society

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