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Lecture - Limits of Spaces

This website contains important announcements regarding the lecture. Also exercise sheets and lecture notes will be posted.


Office hours - Mon and Wed 9:45-10:15 or via appointment

Lecture notes (version 25.07.2019)

Exercise Sheets

Sheet 1 (due 29.04.2019)

Sheet 2 (due 20.05.2019, terminology corrected in Ex 8)

Sheet 3 (due 17.06.2019, correction in Ex 11)

Sheet 4 (due 01.07.2019)

Sheet 5 (due 15.07.2019)

Announcement of the lecture

Limits of Spaces

Lecturer: PD Dr. Martin Kell
Time: Mondays and Wednesdays, 10:15pm to 12pm, starting April 15th 2019, no lecture/exercise on April 17th
Place: S09


In this course basic concepts of metric geometry like geodesics, doubling property of measures and Hausdorff measures are introduced and their properties are investigated. Furthermore, generalized curvature conditions in the sense of Alexandrov and Busemann are studied and the convergence concepts of Gromov-Hausdorff and the ultra convergence are presented and a proof of Gromov's Precompactness Theorem and other stability theorems will be developed.


Analysis I+II and some measure theory.


Jeff Cheeger, David Ebin: Comparison Theorems in Riemannian Geometry, AMS 1975.
Dimitri Burago, Yuri Burago, Sergei Ivano: A Course in Metric Geometry, AMS 2001.
Mikhail Gromov: Metric Structures for Riemannian and Non-Riemannian Spaces, Springer 2007.
Stephanie Alexander, Vitali Kapovitch, Anton Petrunin: Alexandrov geometry: preliminary version no. 1, arxiv:1903.08539v1 (2019).