Metric geometry, fall 2013
Metric geometry, fall 2013
Lecturer
Scope
10 cu
Type
Advanced studies
Description
Metric geometry and analysis on metric spaces are nowadays very popular research topics. The purpose of this course is to introduce some basic notions of metric geometry (like various notions of curvature and boundaries of metric spaces), methods, and results.
Prerequisites
Basic and intermediate studies.
Knowledge on Topology II, Real Analysis I, Introduction to Differential Geometry, and Riemannian Geometry would be useful but not necessary.
Lectures
Weeks 36-49, Tuesday 12-14 in room B322, and Thursday 14-16 in room C123. Note: The last lecture is on Thursday, December 5.
Exams
The course can be passed by an exam or by solving home work problems and writing an essay.
Content (tentative)
- Metric spaces, in particular length spaces
- Model spaces
- Alexandrov-spaces
- Non-positively curved metric spaces
- Metric spaces with curvature bounded from below
- CAT(κ)-spaces
- The Cartan-Hadamard theorem
- Gromov-Hausdorff convergence
- Gromov-hyperbolic metric spaces
Bibliography
- M. Bridson, A. Haefliger: Metric Spaces of Non-Positive Curvature, Springer, 1999.
- D. Burago, Y. Burago, S. Ivanov: A Course in Metric Geometry, American Mathematical Society, 2001.
- Gromov: Metric Structures for Riemannian and Non-Riemannian Spaces, Birkhäuser, 1999.
Lecture notes: I. Holopainen: .
Registration
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Exercises
Group | Day | Time | Place | Instructor |
|---|---|---|---|---|
1. | Wednesday | 14-16 | B322 | Juhani Koivisto |
Home work assignments and solutions