Resistance form

Summary

A resistance form is a quadratic energy form on functions on a set which behaves like the energy of an electrical network. It was introduced by Jun Kigami. It gives a common frame to energies on finite networks, on intervals and on fractals such as the Sierpiński gasket. Each resistance form defines a metric, the resistance metric. It generalizes the effective resistance between two nodes of a network. Under mild conditions a resistance form is also a Dirichlet form. So it gives a Laplacian, a heat equation and a diffusion process on the set.