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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Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework [PDF]
International Conference on Learning Representations, 2022 Bridging geometry and topology, curvature is a powerful and expressive invariant. While the utility of curvature has been theoretically and empirically confirmed in the context of manifolds and graphs, its generalization to the emerging domain of ...
Corinna Coupette +2 more
semanticscholar +1 more source
Weighted Ricci curvature in Riemann-Finsler geometry [PDF]
AUT Journal of Mathematics and Computing, 2021 Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold.
Zhongmin Shen
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Radiometric Constraints on the Timing, Tempo, and Effects of Large Igneous Province Emplacement
Geophysical Monograph Series, Page 27-82., 2021 Exploring the links between Large Igneous Provinces and dramatic environmental impact
An emerging consensus suggests that Large Igneous Provinces (LIPs) and Silicic LIPs (SLIPs) are a significant driver of dramatic global environmental and biological changes, including mass extinctions.
Jennifer Kasbohm +2 more
wiley +3 more sources
Frontiers in Aging Neuroscience, 2023 IntroductionGeometry-inspired notions of discrete Ricci curvature have been successfully used as markers of disrupted brain connectivity in neuropsychiatric disorders, but their ability to characterize age-related changes in functional connectivity is ...
Yasharth Yadav +8 more
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Minkowski inequality on complete Riemannian manifolds with nonnegative Ricci curvature [PDF]
Analysis & PDE, 2021 In this paper we consider Riemannian manifolds of dimension at least $3$, with nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset with smooth boundary we establish the validity of an optimal Minkowski Inequality.
L. Benatti +2 more
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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 ...
Thomas Hasanis, Theodoros Vlachos
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Generalized surgery on Riemannian manifolds of positive Ricci curvature [PDF]
Transactions of the American Mathematical Society, 2021 The surgery theorem of Wraith states that positive Ricci curvature is preserved under surgery if certain metric and dimensional conditions are satisfied.
Philipp Reiser
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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.
Peter F. Stadler +6 more
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On the Almost $\eta-$Ricci Solitons on Pseudosymmetric Lorentz Generalized Sasakian Space Forms
Universal Journal of Mathematics and Applications, 2023 In this paper, we consider Lorentz generalized Sasakian space forms admitting almost $\eta-$Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of \ Lorentz generalized Sasakian space forms admitting $\eta-$Ricci soliton have ...
Mehmet Atçeken, Tuğba Mert
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