Organisation: Prof. Werner Ballmann, Stéphane Félix

Time and place: Friday 14:15, LWK 008, from 16th october on.
Discussion of the subject: Friday 16.10.09, 14:15

Prerequisites: Basics on geometry of surfaces / riemannian manifolds.

Content: Hyperbolic space, hyperbolic manifolds, Teichmüller space, Mostow rigidity theorem, simplicial volume, Gromov norm, Margulis lemma.

Program:

1. (Öznur Albayrak, 23.10.09) Chapter A of [1]: Introduction to hyperbolic space and first properties: models, geodesics, isometries and their classification, curvature.
2. (Peter Kreyßig, 30.10.09) Harmonische Mannigfaltigkeiten und die Lichnerowicz Vermutung / Harmonic manifolds and the Lichnerowicz conjecture (diploma thesis)
3. (Peter Kreyßig, 6.11.09) Chapter B.1-3: Hyperbolic/flat/elliptic on manifolds as quotients, pants decomposition, Gauss-Bonnet for compact surfaces.
4. (Jan Kinne, 13.11.09) Atiyah Gamma Index Satz bei kokompakter Gruppenwirkung (diplomarbeit)
5. (Shimpei Takahashi, 27.11.09) Chapter C.1: Mostow Rigidity Theorem: Extension of pseudo-isometries.
6. (Stefan Mehner, 4.12.09) Chapter C.2: Mostow Rigidity Theorem: Volume of ideal simplices, Gromov Norm.
7. (Steffen Weil, 11.12.09) Metric Foliations in Space Forms (diploma thesis)
8. (Stéphane Félix, 18.12.09) Chapter C.3: Mostow Rigidity Theorem: proof.
9. (Robert Nabiullin, 22.1.10) Sobolev Spaces and the Dirichlet Principle for Metric Space Targets
10. (Lara Skuppin, 29.1.10) The de Rham Decomposition Theorem
11. (Nikolai Nowaczyk, 5.2.10) Introduction to L_p-Cohomology

References:

• [1] Riccardo Benedetti and Carlo Petronio, Lectures on hyperbolic geometry, Universitext, Springer-Verlag, 1992.
• [2] Jürgen Jost, Compact Riemann surfaces, Universitext, Springer-Verlag, 2006.
• [3] John Ratcliffe, Foundations of hyperbolic manifolds, Graduate Texts in Mathematics, Vol. 149, Springer, 2006.