Math
762 — Spring 2002
Seminar in Geometry
| Instructor: |
José F. Escobar |
| Time: |
TR 10:10-11:25 |
| Room: |
Malott 230 |
This course is a continuation of Math 761.
The main topic of the course will be on conformal deformation of metrics
on a compact manifold. I will show that any compact Riemannian manifold
$(M^n,g)$ with boundary admits a metric of the form $e^{2f}g$ with constant
scalar curvature and minimal boundary. This is known as the Yamabe problem
on manifolds with boundary. Then I will study the problem of finding metrics
with zero scalar curvature and prescribed mean curvature on the boundary.
The above problems are equivalent to finding a solution to a nonlinear
elliptic equation with critical Sobolev exponents. I will discuss different
techniques in solving these kind of elliptic problems.
Other topics could include evolution equations such as Hamilton's Ricci
flow and the mean curvature flow and/or the structure of manifolds with
Ricci curvature bounded below.
Last modified:
April 7, 2003
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