MATS4200 Alexandrov spaces (5 cr)
Learning outcomes
After completing the course the student will
鈥nderstand the definitions of curvature lower bounds in the sense of Alexandrov and can check in easy examples if they are satisfied
鈥now the basic ideas behind the proofs of the main theorems presented in the course.
Study methods
One can complete the course either by:
鈥xercises and course exam or
鈥inal exam
Content
The course is intended as an introduction to Alexandrov spaces with curvature bounded below. We will go through
鈥efinitions and examples of Alexandrov spaces with curvature bounded below
鈥oponogov's theorem (local-to-global property)
鈥aximal diameter and splitting theorems
鈥ishop-Gromov inequality and Gromov's precompactness theorem
鈥trainers and local geometry of Alexandrov spaces
Materials
S. Alexander, V.Kapovitch, A. Petrunin, Alexandrov Geometry (draft available at )
D. Burago, Y. Burago, S. Ivanov: A Course in Metric Geometry, American Mathematical Society, 2001.
Prerequisites
The following courses are preferred but not obligatory
鈥ATS213 Metric Spaces
鈥ATS331 Metric Geometry
鈥ATS111 Measure and Integration Theory 1
鈥ATS112 Measure and Integration Theory 2