A dynamic study of the generalized Cheeger problem: An application to the temporal prediction of landslides and rainfall threshold

This paper presents the dynamic generalized Cheeger concept, which sounds very interesting and may lead to many real-world applications in the future.This paper gives a novel insight into the dynamic generalized Cheeger problem as an application to the temporal prediction and rainfall threshold of landslides.The generalized Cheeger problem has applications in landslide modeling as it can compute the safety factor and collapse domain.Notably, the paper presents an innovative graphical method employing the dynamic generalized Cheeger concept for temporal landslide prediction and rainfall threshold determination.While developing the graphical method for temporal prediction of landslides, all causal factors of landslides are considered, and in the same graphical method, only rainfall as a causal factor of landslides is used for the threshold rainfall determination.The paper provides two numerical illustrations demonstrating the reliability and robustness of the proposed method.Moreover, the paper presents a comparative study aimed at showcasing the effectiveness of the proposed graphical method.The result of the study suggests that the rainfall threshold is lowest for circular domains among all shapes with equal area and highest for equilateral triangular domains among regular polygons of equal area, with decreasing thresholds as polygon side count increases.In conclusion, this paper introduces the dynamic study of the generalized Cheeger problem as a novel approach, proposing a graphical method for predicting temporal landslides and rainfall thresholds, ensuring promising avenues for real-life applications stemming from this dynamic study.