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Scalar curvatures of conformal metrics on Sn
Published online by Cambridge University Press: 22 January 2016
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In this paper we consider the following problem: Given a smooth function K on the n-dimensional unit sphere Sn(n ≥ 3) with its canonical metric g0, is it possible to find a pointwise conformal metric which has K as its scalar curvature? This problem was presented by J. L. Kazdan and F. W. Warner. The associated problem for Gaussian curvature in dimension 2 had been presented by L. Nirenberg several years before.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1995