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FIELD Math: CMC
DATE October 16 (Tue), 2018
TIME 14:00-15:30
PLACE 8309
SPEAKER Shiga, Hiroshige
HOST Hong, Jaehyun
INSTITUTE Tokyo Institute of Technology
TITLE On the quasiconformal equivalence of Riemann surfaces and dynamical Cantor sets
ABSTRACT

In the theory of Teichm\"uller space of Riemann surfaces, we consider the set of Riemann surfaces which are quasiconformally equivalent. Here, we say that two Riemann surfaces are quasiconformally equivalent if there is a quasiconformal homeomorphism between them. Hence, at the first stage of the theory, we have to know a condition for Riemann surfaces to be quasiconformally equivalent.

The condition is quite obvious if the Riemann surfaces are topologically finite. On the other hand, for Riemann surfaces of topologically infinite type, the situation is rather difficult. We consider geometric conditions for the quasiconformal equivalence of open Riemann surfaces.

We also discuss the quasiconformal equivalence of regions which are complements of some Cantor sets, e. g., the limit sets of Schottky groups and the Julia sets of some rational functions.

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