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-Scottís result on incompressible surfaces. Then, we see Meeks-Yauís important solutions to fundamental 3-manifold problems like Dehnís Lemma, Loop and Sphere Theorem via minimal surface methods.