Results 211 to 220 of about 71,917 (238)

Ricci Curvature and Fundamental Group*

Chinese Annals of Mathematics, Series B, 2006
Let \(M\) be a compact Riemannian manifold with negative Ricci curvature. The author shows that if the universal cover of \(M\) has a pole and if any geodesic sphere centered at the pole is convex or concave, then the growth function of the fundamental group is at least exponential.
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Metrics of Negative Ricci Curvature

The Annals of Mathematics, 1994
Using some deformation techniques the author is able to construct Riemannian metrics \(g\) of negative Ricci curvature \(r(g)\) and to prove in this way the following remarkable results: (i) For any \(n \geq 3\) there exist constants \(a(n) > b(n) > 0\) such that any manifold \(M\) with \(\dim M \geq 3\) admits a complete Riemannian metric \(g\) for ...
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Graphs with Positive Ricci Curvature

Graphs and Combinatorics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qiqi Huang, Weihua He, Chaoqin Zhang
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Ricci Curvature and Volume Convergence

The Annals of Mathematics, 1997
The author gives a new integral estimate of distances and angles on manifolds with a given lower Ricci curvature bound. He obtains this estimate via a Hessian estimate and states it in three different forms. Using this, he proves (among other things) the following conjectures: 1.
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Ricci Curvature Comparison

1998
In this chapter we shall introduce some of the fundamental theorems for manifolds with lower Ricci curvature bounds. Two important techniques will be developed: relative volume comparison and weak upper bounds for the Laplacian of distance functions.
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The Ricci Curvature

1998
In this chapter we deal with problems concerning Ricci Curvature mainly: Prescribing the Ricci curvature Ricci curvature with a given sign Existence of Einstein metrics.
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Ricci curvature along rays

Publicationes Mathematicae Debrecen, 2005
The author provides some estimates of the integrals over \([0, t]\) of the Ricci curvature in the direction of \(\gamma '(s)\), \(\gamma\) being a geodesic without conjugate points between \(0\) and \(t\).
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Ricci curvature and measures

Japanese Journal of Mathematics, 2009
This article is based on the 5th Takagi Lectures delivered by Jean-Pierre Bourguignon at the University of Tokyo on October 4 and 5, 2008. It offers the general reader -- even those of us not steeped in Differential Geometry -- a fascinating glimpse and interesting account of the development, during the last thirty years, of the analysis of spaces ...
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The Ricci Curvature Equation

1984
Let g = {gij be a Riemannian metric on a manifold M of dimension n. It is Ricci curvature Rc(g) = {Rij} is given by the formula $$ {R_{{ij}}} = \frac{1}{{2(n - 1)}}{g^{{k2}}}\left[ {\frac{{{\partial ^{2}}}}{{\partial {x^{1}}\partial {x^{k}}}}{g_{{j2}}} + \frac{{{\partial ^{2}}}}{{\partial {x^{j}}\partial {x^{2}}}}{g_{{ik}}} - \frac{{{\partial ^{2}}}
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Forman persistent Ricci curvature (FPRC)-based machine learning models for protein–ligand binding affinity prediction

Briefings in Bioinformatics, 2021
JunJie Wee, Kelin Xia
exaly