Results 61 to 70 of about 406,237 (253)
On the weighted orthogonal Ricci curvature
Journal of Geometry and Physics, 2023 18 ...
Kyle Broder, Kai Tang
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Levi-Civita Ricci-Flat Doubly Warped Product Hermitian Manifolds
Advances in Mathematical Physics, 2022 Let M1,g and M2,h be two Hermitian manifolds. The doubly warped product (abbreviated as DWP) Hermitian manifold of M1,g and M2,h is the product manifold M1×M2 endowed with the warped product Hermitian metric G=f22g+f12h, where f1 and f2 are positive ...
Qihui Ni +3 more
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Condensed Ricci curvature of complete and strongly regular graphs [PDF]
Involve. A Journal of Mathematics, 2019 We study a modified notion of Ollivier's coarse Ricci curvature on graphs introduced by Lin, Lu, and Yau in [11]. We establish a rigidity theorem for complete graphs that shows a connected finite simple graph is complete if and only if the Ricci ...
Vincent Bonini +5 more
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Ricci curvature for parametric statistics via optimal transport [PDF]
Information Geometry, 2018 We define the notion of a Ricci curvature lower bound for parametrized statistical models. Following the seminal ideas of Lott–Sturm–Villani, we define this notion based on the geodesic convexity of the Kullback–Leibler divergence in a Wasserstein ...
Wuchen Li, Guido Montúfar
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Local pinching estimates in 3-dim Ricci flow
, 2013 We study curvature pinching estimates of Ricci flow on complete 3- dimensional manifolds without bounded curvature assumption. We will derive some general curvature conditions which are preserved on any complete solution of 3-dim Ricci flow, these ...
Chen, Bing-Long +2 more
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Geometric and spectral estimates based on spectral Ricci curvature assumptions [PDF]
Journal für die Reine und Angewandte Mathematik, 2018 We obtain a Bonnet–Myers theorem under a spectral condition: a closed Riemannian ( M n , g ) {(M^{n},g)} manifold for which the lowest eigenvalue of the Ricci tensor ρ is such that the Schrödinger operator Δ + ( n - 2 ) ρ {\Delta+(n-2)\rho} is positive
G. Carron, Christian Rose
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The Ricci Curvature on Simplicial Complexes
Theory and Applications of Graphs, 2023 We define the Ricci curvature on simplicial complexes by modifying the definition of the Ricci curvature on graphs, and we prove the upper and lower bounds of the Ricci curvature. These properties are generalizations of previous studies. Moreover, we obtain an estimate of the eigenvalues of the Laplacian on simplicial complexes using the Ricci ...
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Electronic Research ArchiveWe proved that on every Stiefel manifold $ V_2\mathbb{R}^n\cong \operatorname{SO}(n)/\operatorname{SO}(n-2) $ with $ n\ge 3 $ the normalized Ricci flow preserves the positivity of the Ricci curvature of invariant Riemannian metrics with positive Ricci ...
Nurlan A. Abiev
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A Review of and Some Results for Ollivier–Ricci Network Curvature
Mathematics, 2020 Characterizing topological properties and anomalous behaviors of higher-dimensional topological spaces via notions of curvatures is by now quite common in mainstream physics and mathematics, and it is therefore natural to try to extend these notions from
Nazanin Azarhooshang +2 more
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A New Transport Distance and Its Associated Ricci Curvature of Hypergraphs
Analysis and Geometry in Metric Spaces, 2022 The coarse Ricci curvature of graphs introduced by Ollivier as well as its modification by Lin–Lu– Yau have been studied from various aspects. In this paper, we propose a new transport distance appropriate for hypergraphs and study a generalization of ...
Akamatsu Tomoya
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