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MR1707696 35P15 (35J25 58J50)
Ashbaugh, Mark S.; Benguria, Rafael D. A sharp bound for the ratio of the first two Dirichlet eigenvalues of a domain in a hemisphere of $S\sp n$. Trans. Amer. Math. Soc. 353 (2001), no. 3, 1055–1087.
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