MATS4110 Metrics with non-positive curvature (4 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2017-2018, 2018-2019, 2019-2020
Description
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
Learning outcomes
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.
Description of prerequisites
Introductory courses in analysis and topology (MATS213 Metric spaces, MATA255 Vector analysis 1 and
MATA256 Vector analysis 2)
MATA256 Vector analysis 2)
Study materials
"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.
Completion methods
Method 1
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Parts of the completion methods
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