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• W2951781697 abstract "We prove that many complete, noncompact, constant mean curvature (CMC) surfaces $f:Sigma to R^3$ are nondegenerate; that is, the Jacobi operator $Delta_f + |A_f|^2$ has no $L^2$ kernel. In fact, if $Sigma$ has genus zero and $f(Sigma)$ is contained in a half-space, then we find an explicit upper bound for the dimension of the $L^2$ jernel in terms of the number of non-cylindrical ends. Our main tool is a conjugation operation on Jacobi fields which linearizes the conjugate cousin construction. Consequences include partial regularity for CMC moduli space, a larger class of CMC surfaces to use in gluing constructions, and a surprising characterization of CMC surfaces via spinning spheres." @default.
• W2951781697 created "2019-06-27" @default.
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• W2951781697 date "2004-07-09" @default.
• W2951781697 modified "2023-09-27" @default.
• W2951781697 title "On the nondegeneracy of constant mean curvature surfaces" @default.
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