Seminar in Analysis - Fribourg


Seminar Program - Academic Year 2014 - 2015:


Date Program Location
October 29, 2014
13:15 - 15:00 Severine Rigot (Nice)
  "Covering lemmas in the Heisenberg groups"

Abstract: In this talk I will explain the main ideas underlying the construction of a homogeneous distance on the Heisenberg groups for which the Besicovitch covering property (BCP) holds (joint work with E. Le Donne). This covering property is known to be an important tool, being for instance equivalent to the validity of the theorem of differentiation for any Radon measure. To put this result in perspective I will also give criteria implying the non-validity of BCP, showing that in some sense our construction is sharp.
Auditorium 1.309, Sciences de la Terre building
November 4, 2014
15:15 - 17:00 Andrea Schioppa (ETHZ)
  "Vector fields on metric mesure spaces, and 1-rectifiable structure"

Abstract: In this talk I will describe a general approach to differentiaton of real-valued Lipschitz functions defined on metric measure spaces. As an application, I will discuss a quantitative characterization of differentiability spaces in the sense of Cheeger and Keith.
Auditorium 2.73, Physics building
November 11, 2014
15:15 - 17:00 Davide Vittone (Univ. di Padova)
  "Minimizers of the area functional in the Heisenberg group"

Abstract: We consider the area functional for graphs in the sub-Riemannian Heisenberg group and study minimizers of the associated Dirichlet problem. We prove that, under a bounded slope condition on the boundary datum, there exists a unique minimizer and that this minimizer is Lipschitz continuous. We also provide an example showing that, in the first Heisenberg group, Lipschitz regularity cannot be improved even under the bounded slope condition. This is based on a joint work with A. Pinamonti, F. Serra Cassano and G. Treu.
Auditorium 2.73, Physics building
April 23, 2015
15:15 - 17:00 Kai Rajala (Univ. Jyvaskyla)
  "Uniformization of metric surfaces"

Abstract: We discuss a generalization of the classical uniformization theorem to metric spaces that have locally finite Hausdorff 2-measure. Namely, we give a necessary and sufficient condition for such spaces to be quasiconformally equivalent to a euclidean space. We also discuss connections to quasisymmetric parametrization problems.
Auditorium 2.52, Physics building



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