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Some new results on eigenvectors via dimension, diameter, and Ricci curvature

Abstract:

We generalise for a general symmetric elliptic operator the different notions of dimension, diameter, and Ricci curvature, which coincide with the usual notions in the case of the Laplace-Beltrami operators on Riemannian manifolds. If λ 1 denotes the spectral gap, that is the first nonzero eigenvalue, we investigate in this paper the best lower bound on λ 1 one can obtain under an upper bound on the dimension, an upper bound on the diameter, and...

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
Advances in Mathematics
Volume:
155
Issue:
1
Pages:
98-153
Publication date:
2000-10-15
ISSN:
0001-8708
URN:
uuid:8eef7c4e-f91b-4ed1-a68f-ca79c2e45061
Source identifiers:
147250
Local pid:
pubs:147250
Language:
English

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