Convergence of graph Dirichlet energies and graph Laplacians on intersecting manifolds of varying dimensions
The research investigates how graph energies and Laplacians behave when defined on unions of intersecting manifolds with different dimensions. It finds that unnormalized energies only capture variations in the highest dimension, whereas normalized energies converge to a structure capable of adapting to all dimensions simultaneously. This is crucial for machine learning applications involving multi-dimensional data.