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If M is a non-compact Riemannian manifold with Ric>=-(n-1),we know that the first eigenvalue λ(M)<=(n-1)^2/4.What if λ(M)=(n-1)^2/4,then M would be?Are there any paper on this topic?

edited Jan 21 at 6:58

asked Jan 21 at 5:59

jiangsaiyin
335●5

	There is no such upper bound for the first eigenvalue, a flat torus is a counterexample. – Anton Petrunin Jan 21 at 6:20
	Thank you!I should add "M is non-compact" – jiangsaiyin Jan 21 at 6:57

Mohan Ramachandran · Answer 1 · 2013-01-21 19:13:20Z UTC

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Peter Li and Jiaping Wang have a series of papers on the structure of complete manifolds with
positive spectrum .Peter Li also has a survey article on this topic .You can find it on his home page .

answered Jan 21 at 19:13

Mohan Ramachandran
1,191●5●8

classification of non-compact Riemannian manifold with Ric>=-(n-1),and first eigenvalue λ=(n-1)^2/4

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