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A best constant and the Gaussian curvature. (English) Zbl 0603.58056
The author finds conditions on \(f(x)\in C^{\infty}(S^ 2)\) so that it can be made the scalar curvature function of a metric pointwise conformal to the standard metric of \(S^ 2\). He also finds the best (smallest possible) constant in the inequality of J. Moser [Indiana Univ. Math. J. 20, 1077-1092 (1971; Zbl 0203.437)] in connection with the above problem.
Reviewer: S.K.Chatterjea

MSC:
58J99 Partial differential equations on manifolds; differential operators
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