| Résume | In this talk I would like to discuss quantitative stability aspects of the class of Möbius transformations of the sphere among maps in the critical Sobolev space (with respect to the dimension). The case of sphere- and R^n-valued maps will be addressed. In the latter, more flexible setting, unlike similar in flavour results for maps defined on domains of R^n (as for instance in the early works of Reshetnyak), not only a conformal deficit is necessary, but also a deficit measuring the distortion of the sphere under the maps in consideration, which is introduced as an associated isoperimetric deficit. The talk will be based on previous works in collaboration with Stephan Luckhaus and Jonas Hirsch, and more recent ones with Xavier Lamy and Andre Guerra. |
