Entropy Bounds for Embedded Self-shrinkers with Rotational Symmetry

In this talk, we study the space of complete embedded rotationally symmetric self-shrinking hypersurfaces. First, we derive explicit upper bounds for the entropy of all such self-shrinkers. Second, as an application we prove a smooth compactness theorem on the space of all such shrinkers. We also prove that there are only finitely many such self-shrinkers with an extra reflection symmetry. This is a joint work with Ali Muhammad and Niels Martin Møller.