Discrete Curvature

Discrete curvature, a concept extending the notion of curvature from continuous manifolds to discrete structures like graphs and meshes, aims to quantify the local and global geometric properties of these data. Current research focuses on developing algorithms to estimate discrete curvature using various approaches, including those based on Ricci curvature and normal variations, and integrating these estimations into machine learning models, particularly graph neural networks (GNNs). This work is significant because it allows for the incorporation of geometric information into analyses of complex data, improving the performance of algorithms in tasks such as graph classification, manifold learning, and mesh processing.