Diff. Geom, Math. Phys., PDE Seminar: Davi Maximo

We show that for an immersed two-sided minimal surface in R^3, there is a lower bound on the index depending on the genus and number of ends. Using this, we show the nonexistence of an embedded minimal surface in R^3 of index 2, as conjectured by Choe. Moreover, we show that the index of an immersed two-sided minimal surface with embedded ends is bounded from above and below by a linear function of the total curvature of the surface. (This is joint work with Otis Chodosh)