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DTSTART;VALUE=DATE:20140401T171500
DTEND;VALUE=DATE:20140401T171500
UID:5706@agenda.unifr.ch
DESCRIPTION:Given a metric space homeomorphic to a Euclidean space (or a\nsphere, for example) it is natural to ask for geometric parametrization\nwith a homeomorphisms which respect the metric, for example, bilipschitz\nor quasisymmetric maps.\n\nIn 1996 Semmes constructed metric spaces which are homeomorphic to the\nstandard Euclidean 3-space but not admit geometric parametrizations.\nThe construction was surprising, since the metric space is close to a\nEuclidean space from the point of view of measure and geometry. In 2004\nBonk and Kleiner showed that metric two dimensional spheres satisfying\nthe same conditions are in fact quasisymmetric to the standard sphere.\n\nAlthough there are no good geometric homeomorphisms from Semmes' space\nto the Euclidean space, there exist other natural geometric mappings to\nthe Euclidean space by results of Heinonen and Rickman in 2004. These\nmappings give Semmes' space a natural ``branched parametrization''.\n\nSemmes' construction is based on a classical geometric topology. In this\ntalk I will discuss the joint work with Jang-Mei Wu on general framework\nof geometric decomposition spaces and their quasisymmetric\n(non-)parametrizability. I will also discuss recent work with Kai Rajala\nand Jang-Mei on the existence of branched parametrizations in this\ngeneral setting.
SUMMARY:Pekka Pankka (Jyväskylä): From non-parametrization to branched parametrization
CATEGORIES:Colloque / Congrès / Forum
LOCATION:PER 08\, Phys 2.52\, Chemin du Musée 3\, 1700 Fribourg
URL;VALUE=URI:https://agenda.unifr.ch/e/fr/5706
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