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OLLIVIERRICCI CURVATURE AND THE SPECTRUM OF THE
, 2011
"... OllivierRicci curvature and the spectrum of the normalized graph Laplace operator by ..."
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OllivierRicci curvature and the spectrum of the normalized graph Laplace operator by
RICCI CURVATURE OF GRAPHS
, 2010
"... We modify the definition of Ricci curvature of Ollivier of Markov chains on graphs to study the properties of the Ricci curvature of general graphs, Cartesian product of graphs, random graphs, and some special class of graphs. 1 ..."
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Cited by 4 (1 self)
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We modify the definition of Ricci curvature of Ollivier of Markov chains on graphs to study the properties of the Ricci curvature of general graphs, Cartesian product of graphs, random graphs, and some special class of graphs. 1
On the Ricci curvature of normal metrics on
, 2007
"... We show that any normal metric on a closed biquotient with finite fundamental group has positive Ricci curvature. 1 ..."
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We show that any normal metric on a closed biquotient with finite fundamental group has positive Ricci curvature. 1
Aspects of Ricci Curvature
, 1997
"... We describe some new ideas and techniques introduced to study spaces with a given lower Ricci curvature bound, and discuss a number of recent results about such spaces. ..."
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We describe some new ideas and techniques introduced to study spaces with a given lower Ricci curvature bound, and discuss a number of recent results about such spaces.
Ricci curvature and betti numbers
, 1994
"... We derive a uniform bound for the total betti number of a closed manifold in terms of a Ricci curvature lower bound, a conjugate radius lower bound and a diameter upper bound. The result is based on an angle version of Toponogov comparison estimate for small triangles in a complete manifold with a R ..."
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Cited by 5 (2 self)
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We derive a uniform bound for the total betti number of a closed manifold in terms of a Ricci curvature lower bound, a conjugate radius lower bound and a diameter upper bound. The result is based on an angle version of Toponogov comparison estimate for small triangles in a complete manifold with a
RICCI CURVATURE AND YAMABE CONSTANTS
, 2005
"... Abstract. We prove that if (M n g) is a closed Riemannian manifold of dimension n ≥ 3 with volume V and Ricci curvature Ricci(g) ≥ ρ> 0 then the Yamabe constant of the conformal class [g] satisfies Y (M, [g]) ≥ nρV (2/n) ; the equality is achieved if g is an Einstein metric (of Ricci curvature ..."
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Cited by 1 (0 self)
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Abstract. We prove that if (M n g) is a closed Riemannian manifold of dimension n ≥ 3 with volume V and Ricci curvature Ricci(g) ≥ ρ> 0 then the Yamabe constant of the conformal class [g] satisfies Y (M, [g]) ≥ nρV (2/n) ; the equality is achieved if g is an Einstein metric (of Ricci curvature
The Pressure of Ricci Curvature
, 2001
"... (M n , g) be a closed Riemannian manifold and let Kmax be any positive upper bound for the sectional curvature. We prove that P # r 2 # Kmax # # n  1 2 # Kmax , where P (f) stands for the topological pressure of a function f on the unit sphere bundle SM and r(v) is the Ricci curvatur ..."
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(M n , g) be a closed Riemannian manifold and let Kmax be any positive upper bound for the sectional curvature. We prove that P # r 2 # Kmax # # n  1 2 # Kmax , where P (f) stands for the topological pressure of a function f on the unit sphere bundle SM and r(v) is the Ricci
Metrics of positive Ricci curvature on bundles
 Int. Math. Res. Not
"... Abstract We construct new examples of manifolds of positive Ricci curvature which, topologically, are vector bundles over compact manifolds of almost nonnegative Ricci curvature. In particular, we prove that if E is the total space of a vector bundle over a compact manifold of nonnegative Ricci cur ..."
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Cited by 10 (6 self)
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Abstract We construct new examples of manifolds of positive Ricci curvature which, topologically, are vector bundles over compact manifolds of almost nonnegative Ricci curvature. In particular, we prove that if E is the total space of a vector bundle over a compact manifold of nonnegative Ricci
MANIFOLDS WITH kPOSITIVE RICCI CURVATURE
"... Let (M, g) be an ndimensional Riemannian manifold. We say M has kpositive Ricci curvature if at each point p ∈ M the sum of the k smallest eigenvalues of the Ricci curvature at p is positive. We say that the kpositive Ricci curvature is bounded below by α if the sum of the k smallest eigenvalues ..."
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Let (M, g) be an ndimensional Riemannian manifold. We say M has kpositive Ricci curvature if at each point p ∈ M the sum of the k smallest eigenvalues of the Ricci curvature at p is positive. We say that the kpositive Ricci curvature is bounded below by α if the sum of the k smallest eigenvalues
Results 1  10
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1,343