Geometric and spectral estimates based on spectral Ricci curvature assumptions
2020 ◽
Vol 0
(0)
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Keyword(s):
AbstractWe obtain a Bonnet–Myers theorem under a spectral condition: a closed Riemannian {(M^{n},g)} manifold for which the lowest eigenvalue of the Ricci tensor ρ is such that the Schrödinger operator {\Delta+(n-2)\rho} is positive has finite fundamental group. Further, as a continuation of our earlier results, we obtain isoperimetric inequalities from Kato-type conditions on the Ricci curvature. We also obtain the Kato condition for the Ricci curvature under purely geometric assumptions.
2009 ◽
Vol 256
(10)
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pp. 3342-3367
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Keyword(s):
2012 ◽
Vol 2
(1)
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pp. 1-56
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2009 ◽
Vol 159
(2)
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pp. 241-263
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2014 ◽
Vol 24
(1)
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pp. 63-84
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2003 ◽
Vol 203
(2)
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pp. 401-424
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Keyword(s):
2014 ◽
Vol 47
(29)
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pp. 295204
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2020 ◽
Vol 41
(3)
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pp. 419-440