Speakers
- The following speakers are confirmed:
- Bill Meeks (UMass-Amherst)
- Title: Progress in the theory of CMC surfaces in locally homgeneous 3-manifolds X
- Abstract:
I will go over some recent work that I have been involved in on surface geometry in complete locally homogeneous 3-manifolds X. In joint work with Mira, Perez and Ros, we have been able to finish a long term project related to the Hopf uniqueness/existence problem for CMC spheres in any such X. In joint work with Tinaglia on curvature and area estimates for CMC H>0 surfaces in such an X, we have been working on getting the best curvature and area estimates for constant mean curvature estimates in terms of their injectivity radii and their genus. It follows from this work that if W is a closed Riemannian manifold W then the moduli space of closed, connected, strongly Alexandrov embedded surfaces of constant mean curvature H in an interval [a,b] with a>0 and of genus bounded above by a positive constant is compact. In another direction, in joint work with Coskunuzer and Tinaglia we now know that in complete hyperbolic 3-manifolds N, any complete embedded surface M of finite topology is proper in N if H is at least 1 (this is work with Tinaglia) and for any value of H less than 1 there exists complete embedded nonproper planes in hyperbolic 3-space (joint work with both researchers). In joint work with Adams and Ramos, we have been able characterize the topological types of finite topology surfaces that properly embed in some complete hyperbolic 3-manifold of finite volume (including the closed case) with constant mean curvature H; in fact, the surfaces that we construct are totally umbilic.
- Richard Schoen (UC-Irvine)
- Title: Perspectives on the scalar curvature
- Abstract:
This will be a general talk concerning the role that the scalar curvature plays
in Riemannian geometry and general relativity. We will describe recent work on
extending the known results to all dimensions, and other issues which are being actively
studied.
- Jeff Viacolvsky (UC-Irvine)
- Title: Nilpotent structures and collapsing Ricci-flat metrics on K3
surfaces
- Abstract:
I will discuss a new construction of families of Ricci-flat
Kahler metrics on K3 surfaces which collapse to an interval, with
Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a
corresponding singular fibration from the K3 surface to the interval,
with regular fibers diffeomorphic to either 3-tori or Heisenberg
nilmanifolds. This is joint work with Hans-Joachim Hein, Song Sun, and
Ruobing Zhang.
|
