2005/11/30 by Adrian Butscher, Frank Pacard, Butscher, Adrian +1
Mathematics · #53Cxx #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:53Cxx
paper · pdf · doi:10.48550/arxiv.math/0511742
22 pages. Final version improves the statement of the theorem, correct some errors and improves the presentation. Accepted for publication by Annali SNS Pisa
arxiv created 2006/11/15 · arxiv updated 2009/12/01
The Clifford tori in the 3-sphere are a one-parameter family of flat, two-dimensional, constant mean curvature (CMC) surfaces. This paper demonstrates that new, topologically non-trivial CMC surfaces resembling a pair of neighbouring Clifford tori connected at a sub-lattice consisting of at least two points by small catenoidal bridges can be constructed by perturbative PDE methods. That is, one can create an approximate solution by gluing a rescaled catenoid into the neighbourhood of each sub-lattice point; and then one can show that a perturbation of this approximate submanifold exists which satisfies the CMC condition.