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- W2794014793 abstract "In this survey, we study three different notions of curvature that are defined on graphs, namely, combinatorial curvature, Bakry-Emery curvature, and Ollivier's Ricci curvature. For each curvature notion, the definition and its motivation from Riemannian geometry will be explained. Moreover, we bring together some global results and geometric concepts in Riemannian geometry that are related to curvature (e.g. Bonnet-Myers theorem, Laplacian operator, Lichnerowicz theorem, Cheeger constant), and then compare them to the discrete analogues in some (if not all) of the discrete curvature notions. The structure of this survey is as follows: the first chapter is dedicated to relevant background in Riemannian geometry. Each following chapter is focussing on one of the discrete curvature notions. This survay is an MSc dissertation in Mathematical Sciences at Durham University." @default.
- W2794014793 created "2018-03-29" @default.
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- W2794014793 date "2018-03-23" @default.
- W2794014793 modified "2023-09-27" @default.
- W2794014793 title "Combinatorial, Bakry-Émery, Ollivier's Ricci curvature notions and their motivation from Riemannian geometry" @default.
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- W2794014793 hasPublicationYear "2018" @default.
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