On the nondegeneracy of constant mean curvature surfaces

Nick Korevaar, Rob Kusner, Jesse Ratzkin

We prove that many complete, noncompact, constant mean curvature (CMC) surfaces $f:\Sigma \to {\mathbb{R}}^3$ are nondegenerate; that is, the Jacobi operator ${\Delta }_f+|A_f{|}^2$ has no $L^2$ kernel. I…