Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Ivan Izmestiev
Technische Universität Berlin
Infinitesimal rigidity of convex surfaces and variations of the Hilbert-Einstein functional
Infinitesimal rigidity of smooth strictly convex surfaces is a classical result proved by Liebmann, Blaschke,
and Weyl about 100 years ago. We give a new proof of it by studying the second variation of the Hilbert-
Einstein functional on a class of warped product metrics. We also discuss some perspectives concerning
a new approach to the Weyl problem and infinitesimal rigidity of Einstein manifolds with boundary.
Literatur
Izmestiev, I. (2011). Infinitesimal rigidity of convex surfaces through the second derivative of the Hilbert-
Einstein functional II: Smooth case. arXiv:1105.5067
Ines Kath
Greifswald
Indefinite extrinsic symmetric spaces
We will study symmetric submanifolds of pseudo-Euclidean spaces. A non-degenerate submanifold of a
pseudo-Euclidean space is called symmetric submanifold or extrinsic symmetric space if it is invariant
under the reflection at each of its affine normal spaces. In particular, each extrinsic symmetric space is
an ordinary (abstract) symmetric space. Another characterisation can be obtained in terms of the second
fundamental form. Extrinsic symmetric spaces are exactly those connected complete submanifolds whose
second fundamental form is parallel.
While a nice construction found by Ferus provides a classification of all extrinsic symmetric spaces in
Euclidean ambient spaces, the pseudo-Riemannian situation is much more involved.
We will give a description of extrinsic symmetric spaces in pseudo-Euclidean spaces in terms of the
corresponding infinitesimal objects and discuss the classification problem for these objects.
Christoph Böhm
Universität Münster
Ricci flow in higher dimensions
The long-time behavior of the Ricci flow in dimension three is described very well by the work of Hamilton
and Perelman. In this talk we address on the one hand which corresponding results are known in higher
dimensions, but point out on the other hand limitations of such a programme.
Wolfgang Lück
Universität Bonn
On the Farrell-Jones Conjecture
We give an introduction to the Farrell-Jones Conjecture and its applications. We give a status report. In
particular we will mention the recent result of Bartels-Lück-Reich-Rüping that the conjecture holds for
GL(n,Z) and, more generally, for arithmetic groups over algebraic number fields.
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