Embedded constant mean curvature surfaces in Euclidean three space

Embedded constant mean curvature surfaces in Euclidean three space

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Christine Breiner, Columbia University
Fine Hall 314

Constant mean curvature (CMC) surfaces are critical points to the area functional with an enclosed volume constraint. Classic examples include the round sphere and a one parameter family of rotationally invariant surfaces discovered by Delaunay. In this talk I outline a generalized gluing method we develop that produces infinitely many new examples of embedded CMC surfaces of finite topology. In particular, I explain how we solve the global linearized problem in the presence of possible obstructions and how we handle the remaining higher order terms. Finally, I will mention aspects of the proof we must alter to adapt the method to higher dimensions. This work is joint with Nicos Kapouleas.