A Global Poincaré inequality on Graphs via a Conical Curvature-Dimension Condition
2018 ◽
Vol 6
(1)
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pp. 32-47
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Keyword(s):
Abstract We introduce and study the conical curvature-dimension condition, CCD(K, N), for finite graphs.We show that CCD(K, N) provides necessary and sufficient conditions for the underlying graph to satisfy a sharp global Poincaré inequality which in turn translates to a sharp lower bound for the first eigenvalues of these graphs. Another application of the conical curvature-dimension analysis is finding a sharp estimate on the curvature of complete graphs
2000 ◽
Vol 25
(4)
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pp. 417-436
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2020 ◽
1959 ◽
Vol 11
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pp. 440-451
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2021 ◽
Vol 14
(1)
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pp. 314-326