CRM: Centro De Giorgi
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Sub-riemannian geometry and beyond, III

Rigidity of maps between Carnot groups

speaker: Xiangdong Xie (Bowling Green State University)

abstract: We will present results showing rigidity and regularity of various maps between Carnot groups. The maps include quasiconformal maps and more generally Sobolev maps. Carnot groups appear in several branches of mathematics including geometry and analysis. In particular Carnot groups appear as the boundary at infinity of some negatively curved homogeneous manifolds. Rigidity of quasiconformal maps between Carnot groups corresponds to rigidity of quasi-isometries between negatively curved homogenous manifolds. In the first part of the talk I will give an introduction to the topic, provide the motivation and survey the known results. In the second part I will explain the ideas of some of the proofs. This talk is based on joint works with various authors including Bruce Kleiner, Stefan Muller and Enrico Le Donne.

Thu 22 Jun, 16:30 - 17:30, Aula Dini
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