On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth [PDF]
Calc Var Partial Differ Equ, 2021 In this paper we provide new existence results for isoperimetric sets of large volume in Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth.
Gioacchino Antonelli +3 more
semanticscholar +2 more sources
Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature [PDF]
Nat Commun, 2021 Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes.
Adam Gosztolai, Alexis Arnaudon
semanticscholar +2 more sources
Ollivier-Ricci Curvature-Based Method to Community Detection in Complex Networks [PDF]
Sci Rep, 2019 Identification of community structures in complex network is of crucial importance for understanding the system’s function, organization, robustness and security.
J. Sia, E. Jonckheere, P. Bogdan
semanticscholar +2 more sources
Ricci curvature: An economic indicator for market fragility and systemic risk [PDF]
Sci Adv, 2016 Researchers introduce the geometric concept of curvature toward the application of uncovering systemic risk and market fragility. Quantifying the systemic risk and fragility of financial systems is of vital importance in analyzing market efficiency ...
Romeil Sandhu +2 more
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Measuring robustness of brain networks in autism spectrum disorder with Ricci curvature [PDF]
Sci Rep, 2019 Ollivier–Ricci curvature is a method for measuring the robustness of connections in a network. In this work, we use curvature to measure changes in robustness of brain networks in children with autism spectrum disorder (ASD).
Anish K. Simhal +7 more
semanticscholar +2 more sources
Ricci curvature in dimension 2 [PDF]
Journal of the European Mathematical Society, 2018 We prove that in two dimensions the synthetic notions of lower bounds on sectional and on Ricci curvature coincide.
A. Lytchak, Stephan Stadler
semanticscholar +3 more sources
Non-local interaction in discrete Ricci curvature-induced biological aggregation [PDF]
Royal Society Open ScienceWe investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods.
Jyotiranjan Beuria, Laxmidhar Behera
doaj +2 more sources
On $m$-th root metrics of isotropic projective Ricci curvature [PDF]
AUT Journal of Mathematics and Computing, 2023 The Ricci curvature is introduced by spray on $M^n$. Sprays are deformed to projective sprays with a volume form $dV$ on $M^n$. The projective Ricci curvature is defined as the expression of Ricci curvature with sprays.
Mehran Gabrani +2 more
doaj +1 more source
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
openaire +4 more sources
The equation of prescribed Ricci curvature [PDF]
Bulletin of the American Mathematical Society, 1980 Dennis DeTurck
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