Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy


MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and 
Technical University of Denmark     Building 128                  Department of Chemistry
Building 321                        P.O. Box 49                   University of Copenhagen 
DK-2800 Lyngby                      DK-4000 Roskilde              DK-2100 Copenhagen Ø
Denmark                             Denmark                       Denmark

RIGIDITY CONJCTURES AND THEOREMS

One of the central conjectures concerning the structure of M is that it is locally connected (MLC). On the one hand, this conjecture would complete a topological study of M including a proof of density of hyperbolic maps. On the other hand, it has deep connections with the Mostow-type rigidity phenomenon in hyperbolic geometry. Attempts to prove MLC led to many deep insights in holomorphic dynamics. The main analytical tools come from the theory of conformal invariants and quasi-conformal maps.