Lecturer:
Course Type:
PhD Course
Academic Year:
2012-2013
Period:
March-May
Duration:
60 h
Description:
- Degree theory:
- Topological approach to finite-dimensional problems.
- Sard's Theorem.
- Finite dimensional degree theory and the Brouwer fixed point theorem.
- Topological degree in infinite-dimensional Banach spaces.
- The Schauder fixed-point theorem.
- Application to the H-bubble problem:
- Preliminaries on the H-bubble problem: the mean curvature of a radial graph in Rn over the unit sphere.
- Existence results from Treibergs-Wei [J.Diff.Geom. 1983], Gerhardt [J.Diff.Geom. 1988], Caldiroli-Gullino [J. Fix. Point Theory Appl.], to appear.
- The case n=2: the variational approach to the H-loops problem for circles in R2: an existence result via min-max and degree arguments.
- Further applications to semilinear nonlinear differential equations will be presented, depending on students' interests and time availability.
Research Group:
Location:
A-133