Si (M, g) est une variete de Riemann complete de courbure scalaire non positive S satisfaisant S(x)≤−e<0 pour x∈M/M 0 , ou M 0 est un ensemble compact, alors il y a une metrique conforme complete g~ de courbure scalaire S~≡−1
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Avilés et al. (1988) studied this question.
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