MATS4110 Metrics with non-positive curvature (4 cr)
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.
Study methods
regular homework assignments, final exam
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
Materials
"Metric spaces of non-positive curvature" by Bridson and Haefliger.
V盲is盲l盲, 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鈥�346.
Bonk, Mario and Bruce Kleiner. Quasisymmetric parametrizations of two-dimensional metric spheres. Invent. Math. 150 (2002), no. 1, 127鈥�183.
Prerequisites
Introductory courses in analysis and topology (MATS213 Metric spaces, MATA255 Vector analysis 1 and
MATA256 Vector analysis 2)