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MR1451597 (2000c:53040) 53C21 (34C10 35J60 53C42 58J50)
do Carmo, Manfredo P.; Zhou, Detang Eigenvalue estimate on complete noncompact Riemannian manifolds and applications. Trans. Amer. Math. Soc. 351 (1999), no. 4, 1391–1401.
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