University of California, Irvine
Department of Mathematics
Differential Geometry Seminar
Spring 2002, MSTB 254, Tuesdays 4-5pm
Previous Seminar | Future Seminar
| Date | Time | Speaker | Title |
| April 9, 2002 | 4:00PM | Ben Chow (UCSD) |
Hamilton's Injectivity Radius Estimate for the Ricci Flow |
| April 11, 2002 | 10:00AM (MSTB256) |
Yanyan Li (Rutgers) (joint with Analysis Seminar) |
On some conformally invariant fully nonlinear equations |
| April 16, 2002 |
4:00PM
|
David Hoffman (MSRI) |
Flat cone metrics and embedded minimal surfaces |
| April 23, 2002 | 4:00PM | Igor Belegradek (Caltech) |
On almost nonnegative Ricci curvature |
| April 30, 2002 | 4:00PM | Andrey Todorov (UCSC) |
Regularized Determinants and Shafarevich's Types Finiteness Conjectures for CY Manifolds |
| May 7, 2002 | 4:00PM | Jianguo Cao (Notre Dame) (joint with analysis seminar) |
Compact manifolds with nonpositive curvature and small volume |
| May 14, 2002 | 4:00PM | (cancelled) | (cancelled) |
| May 28, 2002 | 4:00PM | Chikako Mese (Conn. College) |
Morgan-Shalen compactification via harmonic maps |
See the pdf file.
In this lecture, we discuss compact manifolds with nonpositive curvature and small volume. Among other things, we present a new result (jointly with Cheeger and Rong) on classification of compact manifolds with nonpositive curvature and small volume.
More precisely, we show that there exists a constant a(n) > 0 such that if a compact Riemannian manifold M^n has sectional curvature, -1 =< K =< 0 and injectivity radius at each point of M^n is less than a(n), then M^n must be isometric to a generalized graph-manifold. In particular, for each point p in M^n, there exists a local isometric splitting with nontrivial flat tori factor. Consequently, one can show that the Gromov's invariant and Euler number of such a manifold is zero.
We discuss harmonic maps from two dimensional polyhedral domains into non-positively curved metric spaces. As an application, we give a harmonic maps description of the boundary points of the Morgan-Shalen compactification of the SL(2,C) character varieties.