Analysis and Geometric Analysis Seminar
Modulus of path families has long been a tool in the theory of quasiconformal maps. I will discuss a recent joint work with Ilmari Kangasniemi regarding a different definition for the modulus of a family of surfaces. Our definition uses differential forms as densities, opposed to positive measurable functions. I will present a general duality theorem for homology families of Lipschitz surfaces. The differential form modulus can also be used to characterize whether a form is closed or exact.