On the topology and index of minimal surfaces

On the topology and index of minimal surfaces

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Davi Maximo, Stanford University
Fine Hall 314

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)