Results 1 to 10 of about 1,071 (142)
Ollivier Ricci curvature of directed hypergraphs. [PDF]
Sci Rep, 2020 AbstractMany empirical networks incorporate higher order relations between elements and therefore are naturally modelled as, possibly directed and/or weighted, hypergraphs, rather than merely as graphs. In order to develop a systematic tool for the statistical analysis of such hypergraph, we propose a general definition of Ricci curvature on directed ...
Eidi M, Jost J.
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FORMAN–RICCI CURVATURE FOR HYPERGRAPHS [PDF]
Advances in Complex Systems, 2021 Hypergraphs serve as models of complex networks that capture more general structures than binary relations. For graphs, a wide array of statistics has been devised to gauge different aspects of their structures. Hypergraphs lack behind in this respect.
Wilmer Leal +3 more
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On Scalar and Ricci Curvatures [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 The purpose of this report is to acknowledge the influence of M. Gromov's vision of geometry on our own works. It is two-fold: in the first part we aim at describing some results, in dimension 3, around the question: which open 3-manifolds carry a complete Riemannian metric of positive or non negative scalar curvature?
Besson, Gérard, Gallot, Sylvestre
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Introducing quantum Ricci curvature [PDF]
Physical Review D, 2018 43 pages, 27 ...
Klitgaard, N.F. +3 more
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Ricci curvature and volume growth [PDF]
Pacific Journal of Mathematics, 1991 The well known Bishop-Gromov inequality for the volume growth of balls in a Riemannian manifold \(M\) has an analogue for tubes around a compact totally geodesic submanifold \(L\subset M\), but instead of a lower Ricci curvature bound one has to assume a lower bound \(\kappa\) for the radial sectional curvatures of \(M\) with respect to \(L\).
Strake, M., Walschap, G.
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Steady Ricci solitons with horizontally ϵ-pinched Ricci curvature
Science China Mathematics, 2020 Corollary 3.11 is ...
Deng, Yuxing, Zhu, Xiaohua
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Boundary effect of Ricci curvature [PDF]
Journal of Differential Geometry, 2016 On a compact Riemannian manifold with boundary, we study how Ricci curvature of the interior affects the geometry of the boundary. First we establish integral inequalities for functions defined solely on the boundary and apply them to obtain geometric inequalities involving the total mean curvature.
Miao, Pengzi, Wang, Xiaodong
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Ricci curvature and orientability [PDF]
Calculus of Variations and Partial Differential Equations, 2017 49 pages.
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Ricci curvature and betti numbers [PDF]
Journal of Geometric Analysis, 1997 18pages ...
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Ricci curvature and minimal submanifolds [PDF]
Pacific Journal of Mathematics, 2001 This paper studies isometric minimal immersions \(f\) of a complete orientable Riemannian \(n\)-manifold \(M\) into the round sphere \(S^{n+k}\). Theorem A: If \(k=1\), then the supremum of Ric\((M)\) is \(\geq n-2\). Moreover, if the supremum equals \(n-2\), then if \(n\) is odd, the universal cover of \(M\) is homomorphic to \(S^n\), and if \(n\) is ...
Hasanis, T., Vlachos, T.
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