ICM Satellite Conference            September 1 - 4,  2006

Geometric Analysis and  PDEs

Istituto Piccole Ancelle di Cristo Re, Naples, Italy



  The purpose of the meeting is to provide a forum to explore the interplay between partial differential equations (PDEs) and the geometric theory of mappings.
 
  The generalizations of Cauchy-Riemann and Beltrami equations to higher dimensions are at the heart of modern Geometric Function Theory. The category of maps that one usually considers are mappings with finite  distortion. When the  distortion is bounded, these mappings are quasiregular mappings quasiconformal  if injective.  The potential theory associated to these mappings is governed by  a class of non-linear elliptic equations modeled on the  p-Laplacian that are called A-harmonic equations. The components of the mappings under consideration and the logarithm of their modulus are A-harmonic functions for an appropriate choice of A. This allows for the use of potential theoretic tools to study mappings of finite distortion.
 
  Far reaching generalizations of many aspects of this theory have been considered in more general geometric settings like Riemannian manifolds and nilpotent (Carnot) groups. Subelliptic versions of convexity, solutions to Hamilton Jacobi equations, and p-harmonic functions have been studied in recent  years.
 
  The  purpose of the workshop is to bring together people working  in all these different but related areas,  and at the same time, both stimulate an interdisciplinary discussion on these topics and review recent developments.