Geometric Analysis and Topology Seminar

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Gluing Constructions for Constant Mean Curvature (Hyper)Surfaces

Speaker: Christine Breiner, Fordham

Location: Warren Weaver Hall 517

Date: Friday, March 14, 2014, 11 a.m.

Synopsis:

Constant mean curvature (CMC) surfaces are critical points to the area functional subject to an enclosed volume constraint. Classic examples include the round sphere, the cylinder, and a family of rotationally symmetric solutions discovered by Delaunay. More than 150 years later, Kapouleas determined a generalized gluing construction that produced infinitely many new examples of CMC surfaces. Building on and refining this work, we produce infinitely many new embedded CMC surfaces and hypersurfaces. In this talk I will outline the main steps of the gluing construction and explain some of the difficulties involved in solving such a problem. This work is joint with N. Kapouleas.