Seminar

Constant mean curvature (CMC) surfaces are critical points for the area functional, subject to an enclosed volume constraint. Classical examples include spheres and cylinders. Until the late 1980's the only other known examples were the Wente torus and the rotationally symmetric surfaces of Delaunay. In 1990, Kapouleas developed a gluing construction that produced infinitely many new examples of CMC surfaces. In this talk, we will discuss an extension of these ideas that produces infinitely many CMC hypersurfaces without any presumed symmetries. The talk will begin at an introductory level and much attention will be paid to explaining how ``force balancing" plays a role in these constructions. This work is joint with N. Kapouleas.