 
Summary: MATH 241C Topics in Differential Geometry
Spring 2011, MWF 2:002:50, SH 4607
Instructor: Prof. Rick Ye
Office: SH 6509, Tel. 8938034, email: yer@math.ucsb.edu
Office Hours: MWF 1:001:50, SH6509.
Topics in Mathematical Theory of General Relativity
A number of fundamental results have been obtained in the mathematical
theory of general relativity and related geometric fields. These results play
an important role in the theory itself, and have also triggered new devel
opments in geometric analysis. In this course we are planning to cover the
following topics (not necessarily in this order):
1. First variation and second variation of area.
2. Toplogy and geometry of stable minimal surfaces in 3manifolds of non
negative scalar curvature. This is an independent direction, but is intimately
related to the topics of asymptotically flat manifolds.
3. ADM mass and positive mass theorems of SchoenYau and Witten. The
former uses minimal surfaces and nonlinear analysis, while the latter is based
on spin geometry and linear analysis.
4. Constructions of unique foliation by constant mean curvature spheres on
asymptotically flat manifolds, which provides a unique geometric structure
