Quasiconformal geometry of fractals

• Autores: Mario Bonk
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé, Javier Soria de Diego, Juan Luis Varona Malumbres, Joan Verdera, Vol. 2, 2006, ISBN 978-3-03719-022-7, págs. 1349-1374
• Idioma: inglés
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• Resumen

  • Many questions in analysis and geometry lead to problems of quasiconformal geometry on non-smooth or fractal spaces. For example, there is a close relation of this subject to the problem of characterizing fundamental groups of hyperbolic 3-orbifolds or to Thurston�s characterization of rational functions with finite post-critical set.

    In recent years, the classical theory of quasiconformal maps between Euclidean spaces has been successfully extended to more general settings and powerful tools have become available.

    Fractal 2-spheres or Sierpi´nski carpets are typical spaces for which this deeper understanding of their quasiconformal geometry is particularly relevant and interesting.