Analysis and Geometric Analysis Seminar

Eden PrywesPrinceton University
Differential Form Modulus of Lipschitz Homology Classes

Monday, October 31, 2022 - 2:40pm
Malott 406

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.