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MR831200 (87i:53092) 53C45 (49F99 58G30)
Oliker, V. I. The problem of embedding $S\sp n$ into ${\bf R}\sp {n+1}$ with prescribed Gauss curvature and its solution by variational methods. Trans. Amer. Math. Soc. 295 (1986), no. 1, 291–303.
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