SMS scnews item created by Boris Lishak at Mon 5 Nov 2018 1630
Type: Seminar
Distribution: World
Calendar1: 7 Nov 2018 1200-1300
CalLoc1: Carslaw 535A
CalTitle1: Le Donne -- Boundaries, conformal maps, and sub-Riemannian geometry
Auth: borisl@dora.maths.usyd.edu.au

Geometry and Topology Seminar

Boundaries, conformal maps, and sub-Riemannian geometry

Enrico Le Donne (Jyvaskyla)

Please join us for lunch at 1 p.m.

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.


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