Arbeitsgruppe Differentialgeometrie
(Prof. Dr. B. Wilking, Prof. Dr. C. Böhm)
Vorträge im Oberseminar Differentialgeometrie, SS 2010
| Datum |
Vortragender |
Titel |
|
| 12.04.2010 | Cabezas-Rivas, Esther (WWU Münster) |
Harnack inequalities for
Ricci flow in the light of the Canonical Expanding Soliton ABSTRACT: In this talk, we introduce the notion of Canonical Expanding Ricci Soliton. Roughly speaking, given any Ricci flow on a manifold M over a time interval I, we imagine the time direction as an additional space direction and construct an expanding Ricci soliton on M x I with respect to a completely new time direction. Then we will show how to apply such a new construction to derive new Harnack inequalities for Ricci flow. This viewpoint also gives geometric insight into the existing Harnack inequalities of Hamilton and Brendle. |
|
| 19.04.2010 | Cabezas-Rivas, Esther (WWU Münster) |
Volume-preserving flow by
powers of the m-th mean curvature ABSTRACT: In this talk, we will analyse the evolution of closed hypersurfaces in the Euclidean space for which a contraction by a power of the m-th mean curvature (which can be regarded as a generalization of the mean, Gauss and scalar curvatures) is balanced by a spatially constant expansion to keep the volume fixed. We concentrate on velocities with degree of homogeneity greater than 1. Asking initially that the principal curvatures at each point lie in a suitably small cone about the umbilic line, we prove: (a) preservation of such a pinching condition, (b) existence of the solution for all time, and (c) exponential and smooth convergence to a round sphere. |
|
| 26.04.2010 | Wörner, Andreas (WWU Münster) |
A splitting theorem for nonnegatively curved Alexandrov spaces
|
|
| 03.05.2010 | Bielawski, Roger (University of Leeds) |
Complete Ricci-flat Kaehler metrics on vector bundles | |
| 10.05.2010 | Jablonski, Michael (University of Oklahoma) |
Solvable Lie groups and left-invariant Einstein metrics |
|
| 17.05.2010 | Leuzinger, Enrico (Universität Karlsruhe, Institut für Technologie) |
The large scale geometry of moduli spaces of Riemann surfaces | |
| 31.05.2010 |
Galaz Garcia, Fernando (WWU Münster) |
Circle actions on 4-dimensional biquotients | |
| 07.06.2010 |
Grosse-Braukmann, Karsten (TU Darmstadt) |
Constant mean curvature surfaces and projective
structures |
|
| 14.06.2010 |
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| 21.06.2010 |
Quast, Peter (Uni Augsburg) |
Complex structures and inclusion chains of symmetric spaces | |
| 28.06.2010 |
Pohl, Anke (ETH Zürich) |
Maass cusp forms for Hecke triangle groups, closed geodesics, and invariant measures Abstract: Maass cusp forms are certain eigenfunctions of
the Laplace-Beltrami operator which are of particular interest in number theory
and physics. If $H$ denotes the upper half plane and $\Gamma$ is a Hecke
triangle group, then the length spectrum of closed geodesics on
$\Gamma\backslash H$ is generated by the Selberg zeta function. The Selberg
trace formula shows that the zeros of the Selberg zeta function and the
eigenvalues of Maass cusp forms are in bijection. For the Hecke triangle group $\PSL(2,\Z)$ combination of
work by D. Mayer, and Lewis and Zagier provides an explicit isomorphism between
Maass cusp forms and eigenfunctions of a transfer operator (evolution operator)
which arises from a symbolic dynamics for the geodesic flow on
$\PSL(2,\Z)\backslash H$. These eigenfunctions encode, via the Fredholm
determinant of the transfer operator, the zeros of the Selberg zeta function. As
a by-product, they prove the relation between zeros and eigenvalues avoiding
the Selberg trace formula. I will report on work in progress joint with Martin
Möller towards a uniform generalization of this so-called transfer operator
method to all cofinite Hecke triangle groups. |
|
| 05.07.2010 |
Wilking, Burkhard (WWU Münster) |
Some new a priori estimates for manifolds with lower
Ricci curvature bound |
|
| 12.07.2010 |
Ziller, Wolfgang (University of Pennsylvania) |
Title: Obstructions to
positive curvature Abstract: We will show that one of the proposed candidates for cohomogeneity one manifolds with positive sectional curvature does not carry an invariant metric with positive curvature. |
|
| 19.07.2010 |
Shin-ichi Ohta (Kyoto University/MPIM Bonn) |
"Ricci curvature and optimal transport |