Worldwide Sites

You have been detected as being from . Where applicable, you can see country-specific product information, offers, and pricing.

Change country/language X

Keyboard ALT + g to toggle grid overlay

Doubling constructions for constant mean curvature tori in the 3-sphere

Adrian Butscher, F. Pacard

Annali della Scuola Normale Superiore de Pisa - Classe di Scienza
2006

Abstract

The Clifford tori in the 3-sphere constitute a one-parameter family of flat, two-dimensional, constant mean curvature (CMC) submanifolds. 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 a submanifold that has almost everywhere constant mean curvature by gluing a re-scaled catenoid into the neighbourhood of each point of a sub-lattice of the Clifford torus; and then one can show that a constant mean curvature perturbation of this submanifold does exist.

Related Publications

Related Projects

Heading

Descriptive text. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt magna aliqua in reprehenderit.

Heading

Descriptive text. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt magna aliqua in reprehenderit.

Heading

Descriptive text. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt magna aliqua in reprehenderit.