MATS4110 Metrics with non-positive curvature (4 op)
Opinnon taso:
Syventävät opinnot
Arviointiasteikko:
0-5
Suorituskieli:
englanti
Vastuuorganisaatio:
Matematiikan ja tilastotieteen laitos
Opetussuunnitelmakaudet:
2017-2018, 2018-2019, 2019-2020
Kuvaus
Content
-Fundamentals: metric spaces, geodesics, arc length, hyperbolic space
-delta-hyperbolic spaces, the Gromov boundary, visual metric, conjectures of Cannon, Kapovich--Kleiner
-quasisymmetric mappings and uniformization of metric spaces
Completion methods
regular homework assignments, final exam
Osaamistavoitteet
The goal of this course is to provide the mathematical foundations needed for understanding the body of recent research connecting (1) analysis on metric spaces and (2) geometric group theory.
Esitietojen kuvaus
MATS213 Metriset avaruudet, MATA255 Vektorianalyysi 1 ja MATA256 Vektorianalyysi 2
Oppimateriaalit
"Metric spaces of non-positive curvature" by Bridson and Haefliger.
Väisälä, Jussi. Lectures on n-dimensional quasiconformal mappings. Lecture Notes in Math. 229, Springer-Verlag, Berlin, Heidelberg, New York 1971.
Tukia, Pekka. On quasiconformal groups. J. Analyse Math. 46 (1986), 318–346.
Bonk, Mario and Bruce Kleiner. Quasisymmetric parametrizations of two-dimensional metric spheres. Invent. Math. 150 (2002), no. 1, 127–183.
Väisälä, Jussi. Lectures on n-dimensional quasiconformal mappings. Lecture Notes in Math. 229, Springer-Verlag, Berlin, Heidelberg, New York 1971.
Tukia, Pekka. On quasiconformal groups. J. Analyse Math. 46 (1986), 318–346.
Bonk, Mario and Bruce Kleiner. Quasisymmetric parametrizations of two-dimensional metric spheres. Invent. Math. 150 (2002), no. 1, 127–183.
Suoritustavat
Tapa 1
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Suoritustapojen osat
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