4:00 p.m., Monday (March 24th)
Department of Mathematics
University of California, Irvine
The geometry and topology of manifolds with positive spectrum
In this talk, I will discuss my recent joint work with
Jiaping Wang. The class of manifolds being considered are complete
manifolds whose Ricci curvature is bounded from below and the bottom of
the spectrum of the Laplacian is positive. An important quantity is
the ratio between the lower bound of the Ricci curvature and the bottom
of the spectrum. There are two critical values for this ratio, each
one gives a metric rigidity theorem and also some topological
restriction on this class of manifolds. In particular, one can derive
a generalization of a theorem of Witten and Yau.
Refreshments will be served at 3:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).