Doubling constant mean curvature tori in S3

Doubling Constant Mean Curvature Tori in S

The Clifford tori in S constitue 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 ...

Doubling constant mean curvature tori in S 3

The Clifford tori in S3 constitute a one-parameter family of flat, twodimensional, 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...

Generalized Doubling Constructions for Constant Mean Curvature Hypersurfaces in S

The sphere S contains a simple family of constant mean curvature (CMC) hypersurfaces of the form Λp,q a ≡ S p(a)×Sq( √ 1− a) for p+ q+1 = n and a ∈ (0, 1) called the generalized Clifford hypersurfaces. This paper demonstrates that new, topologically non-trivial CMC hypersurfaces resembling a pair of neighbouring generalized Clifford tori connected to each other by small catenoidal bridges at a ...

Lower bounds for Morse index of constant mean curvature tori

In the paper, three lower bounds are given for the Morse index of a constant mean curvature torus in Euclidean 3-space, in terms of its spectral genus g. The first two lower bounds grow linearly in g and are stronger for smaller values of g, while the third grows quadratically in g but is weaker for smaller values of g.

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form