### Abstract:

The objective of this talk is to give a new point of view for the validity of Fefferman's mapping theorem from 1974. This result states that a biholomorphism between two smoothly bounded strictly pseudoconvex domains in C^n extends as a smooth diffeomorphism between their closures.

Following ideas from Gromov, Mostow, and Pansu, we discuss a method of proof in the context of quasi-conformal geometry. In particular, we show that every isometry between smoothly bounded strictly pseudoconvex domains is 1-quasi-conformal with

respect to the sub-Riemannian distance defined by the Levi form on the boundaries.

Subsequently, a PDE argument shows that such maps are smooth. This method was proposed by M. Cowling, and it has been implemented in collaboration with L. Capogna, G. Citti, and A. Ottazzi.

Speaker

Enrico Le Donne

Research Area
Affiliation

Research Fellow of the Finnish Academy, Associate professor (Yliopistonlehtori) at University of Jyväskylä, Finland

Date

Thu, 18/10/2018 - 12:00pm

Venue

OMB-229, Old Main Building