We show that for an immersed two-sided minimal surface in R3, 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 R3 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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology