Bochner's Method for Cell Complexes and Combinatorial Ricci Curvature

By Robin Forman. Discrete & Computational Geometry, 2003

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Bakry–Émery curvature and diameter bounds on graphs (2016, background): “However, for many discrete curvature notions there is already a BonnetMyers-type result established (for sectional curvature on planar graphs, see [6, 10, 14, 22], and for Ollivier-Ricci-curvature, see [20], and for Forman’s discrete Ricci curvature, see [8]).”
Volume growth, spectrum and stochastic completeness of infinite graphs (2011, background): “Several other notions of curvature have been introduced for planar graphs [4, 5, 31], cell complexes [21], and general metric measure spaces [8, 43, 45, 49, 50].”
Li–Yau inequality on finite graphs via non-linear curvature dimension conditions (2014, background): “A notion of Ricci curvature on cell complexes by counting neighboring cells is presented in [11].”
Higher order learning with graphs (2006, background): “For a more formal presentation of the material in this section, we refer the reader to (Munkres, 1984; Chung, 1993; Chung, 1997; Forman, 2003).”
Mass transportation and rough curvature bounds for discrete spaces (2009, background): “Forman has introduced in [3] a different notion of combinatorial Ricci curvature for cell complexes.”