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arXiv · 2606.04007

Forman--Ricci Curvature for Irregular Convex Mosaics

Abhyudaya Gupta·Sayak Mukherjee·Kuldeep Saha
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Abstract

Forman has defined a discrete version of the Ricci curvature on Riemannian manifolds, known as the Forman--Ricci curvature. The Forman--Ricci curvature has found significant applications in several pattern recognition problems occurring in natural sciences. Domokos and Langi, on the other hand, have defined a notion of irregularity for convex mosaics, which has also found remarkable applications to the geological problem of fractures in rocks. We define a modification of the classical Forman--Ricci curvature for irregular convex mosaics and demonstrate how they can be used to distinguish between various fractures or cracking patterns appearing in nature.

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Abhyudaya Gupta, Sayak Mukherjee, Kuldeep Saha. 2026-05-28. Forman--Ricci Curvature for Irregular Convex Mosaics. https://arxiv.org/abs/2606.04007

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