University of California, Irvine
Department of Mathematics
Differential Geometry Seminar
Fall 2002, MSTB 254, Tuesdays 4-5pm
Previous Seminar | Future Seminar
| Date | Time | Speaker | Title |
| Tuesday, Oct 8 | 4:00pm | Xiaofeng Sun (UCI) |
On the Weil-Petersson Geometry |
| Tuesday, Oct 22 | 4:00pm | Zhuang-dan Guan (UCR) |
Jacobi Fields and Geodesic Stability |
| Tuesday, Oct 29 | 4:00pm | Yiu-ming Lo (UCI) |
A vanishing theorem on manifolds of positive spectrum |
| Tuesday, Nov. 12 | 4:00pm | Shu-Cheng Chang (UCSD and Taiwan) |
Existence of Extremal Metrics on Complete Manifolds |
| Tuesday, Nov 19 | 4:00pm | David Glickenstein (UCSD) |
Precompactness of solutions
of the Ricci flow in the absence of injectivity radius estimates |
| Tuesday, Dec. 3 | 4:00pm | Zhiqin Lu (UCI) |
Szego kernel of the unit circle bundle |
I will talk about why the generalized Futaki invariants are
independent of the initial metrics and why they are linearly depend on the
directions of the maximal geodesic rays.
I will also give an outline of some related issue on existence of geodesics
and testing of the geodesic stability.
We will try to generalize a splitting theorem on comformally compact manifolds by C. Leung and T. Wan to manifolds of positive spectrum.
Consider a sequence of pointed n-dimensional complete Riemannian manifolds ${( M_i,g_i(t),O_i )}$ such that $t \in [0,T]$ are solutions to the Ricci flow and $g_i(t)$ have uniformly bounded curvatures and derivatives of curvatures. Richard Hamilton showed that if the initial injectivity radii are uniformly bounded below then there is a subsequence which converges to an n-dimensional solution to the Ricci flow. We prove a generalization of this theorem where the initial metrics may collapse. Without injectivity radius bounds we must allow for convergence in the Gromov-Hausdorff sense to a space which is not a manifold but only a metric space. We then look at the local geometry of the limit to understand how it relates to the Ricci flow.
We will talk about the connections between the Ramadanov Conjecture and the Monge-Ampere type equations.