- Recommended Texts:
- Oprea, Differential Geometry and Its Application, Prentice Hall
Morgan, Riemannian Geometry: A Beginner's Guide, 2nd Ed, A K Peters
Morgan, Geometric Measure Theory: A Beginner's Guide,
2nd Ed, Academic Press
This course will cover variational problems in geometry,
primarily the geometry of surfaces in (euclidean or spherical) space.
Specifically, we will consider problems of minimizing area
(leading to minimal surfaces, or constant-mean-curvature surfaces
if there is a volume constraint) and of minimizing elastic bending
energy (leading to Willmore surfaces), among others. Such surfaces
arise physically in soap films, foams, cell membranes and elsewhere.
For some of these problems, there is not yet enough theory to
get explicit solutions, except numerically.
Students will learn to use the
to find numerical solutions for these geometric optimization problems.