Solvability of the Equation Δ g u + ~ S u σ = Su on Manifolds

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY（1994）

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摘要

For the negative Yamabe invariant and S less-than-or-equal-to 0, we obtain that the equation DELTA(g)u + Su(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 S is positive.

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关键词

YAMABE INVARIANT,1ST EIGENVALUE,0-LEVEL SET,SMOOTH COVERING

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