The Ricci curvature plays an important role in Riemannian geometry. The assumption that the manifold has nonnegative Ricci curvature implies some geometric and topological constraints (For instance, the diameter of the manifold is bounded and so the manifold is compact. This is the famous Bonnet–Myers Theorem). In these notes, we present several approaches to extend this kind of results in the setting of discrete graphs, in particular Cayley graphs of finitely generated groups.
@article{TSG_2019-2021__36__103_0, author = {Herv\'e Pajot}, title = {On the notions of lower {Ricci} curvature bound for discrete graphs}, journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie}, pages = {103--126}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {36}, year = {2019-2021}, doi = {10.5802/tsg.374}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.374/} }
TY - JOUR AU - Hervé Pajot TI - On the notions of lower Ricci curvature bound for discrete graphs JO - Séminaire de théorie spectrale et géométrie PY - 2019-2021 SP - 103 EP - 126 VL - 36 PB - Institut Fourier PP - Grenoble UR - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.374/ DO - 10.5802/tsg.374 LA - en ID - TSG_2019-2021__36__103_0 ER -
%0 Journal Article %A Hervé Pajot %T On the notions of lower Ricci curvature bound for discrete graphs %J Séminaire de théorie spectrale et géométrie %D 2019-2021 %P 103-126 %V 36 %I Institut Fourier %C Grenoble %U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.374/ %R 10.5802/tsg.374 %G en %F TSG_2019-2021__36__103_0
Hervé Pajot. On the notions of lower Ricci curvature bound for discrete graphs. Séminaire de théorie spectrale et géométrie, Tome 36 (2019-2021), pp. 103-126. doi : 10.5802/tsg.374. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.374/
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