Séminaire des Doctorants et Doctorantes

Sobolev maps to manifolds: a generalization of the Jacobian and its applications

by Mr Kai Xiao (ICJ)

Europe/Paris
Fokko du Cloux (ICJ)

Fokko du Cloux

ICJ

Description

In this seminar, I am going to give a short introduction to the topic of Sobolev maps to manifolds.
Starting with the observation that the strong density fails when considering maps that are restricted to take their values on a closed manifold, the following questions arise naturally: (Q1) When does the strong density hold? (Q2) If the strong density fails, how to characterize the maps that can be approximated with smooth maps?
A good candidate to answer (Q2) in special cases is the distributional Jacobian, which detects the topological singularities of the map, so that a map can be approximated if and only if its Jacobian is 0.
We will introduce a generalization of the Jacobian in more general case.