Special Topics Course:

Minimal Surfaces in 3-manifolds

In this course, we will go over some important applications of minimal surface theory in 3-manifold topology. In the first half of the class, we go over the basic notions in minimal surface theory. Then, we will start with basic results on finding canonical representatives of embedded surfaces in 3-manifolds. We study Freedman-Hass-Scott’s result on incompressible surfaces. Then, we see Meeks-Yau’s important solutions to fundamental 3-manifold problems like Dehn’s Lemma, Loop and Sphere Theorem via minimal surface methods.