Minimal Surfaces in the Three-sphere by Doubling the Clifford Torus
نویسنده
چکیده
We construct embedded closed minimal surfaces in the round three-sphere S(1), resembling two parallel copies of the Clifford torus, joined by m small catenoidal bridges symmetrically arranged along a square lattice of points on the torus.
منابع مشابه
MINIMAL SURFACES IN THE THREE-SPHERE BY DOUBLING THE CLIFFORD TORUS By NIKOLAOS KAPOULEAS and SEONG-DEOG YANG
We construct embedded closed minimal surfaces in the round three-sphere S3(1), resembling two parallel copies of the Clifford torus, joined by m2 small catenoidal bridges symmetrically arranged along a square lattice of points on the torus.
متن کاملHonours Projects for 2009
This project concerns an important conjecture which appears to have been solved recently: It concerns minimal surfaces, in particular minimal submanifolds of spheres. It combines PDE and geometry, though the PDE required is not very much. It does involve some basic spectral theory for the Laplacian on a Riemannian manifold. There are many examples known of submanifolds in spheres which are mini...
متن کاملA Proof of the Lawson Conjecture for Minimal Tori Embedded in S
A peculiarity of the geometry of the euclidean 3-sphere S is that it allows for the existence of compact without boundary minimally immersed surfaces. Despite a wealthy of examples of such surfaces, the only known tori minimally embedded in S are the ones congruent to the Clifford torus. In 1970 Lawson conjectured that the Clifford torus is, up to congruences, the only torus minimally embedded ...
متن کاملWillmore Surfaces of Constant Möbius Curvature
We study Willmore surfaces of constant Möbius curvature K in S. It is proved that such a surface in S must be part of a minimal surface in R or the Clifford torus. Another result in this paper is that an isotropic surface (hence also Willmore) in S of constant K could only be part of a complex curve in C ∼= R or the Veronese 2-sphere in S. It is conjectured that they are the only examples possi...
متن کامل5 O ct 1 99 8 Rotations of the three - sphere and symmetry of the Clifford Torus
We describe decomposition formulas for rotations of R and R that have special properties with respect to stereographic projection. We use the lower dimensional decomposition to analyze stereographic projections of great circles in S ⊂ R. This analysis provides a pattern for our analysis of stereographic projections of the Clifford torus C ⊂ S ⊂ R. We use the higher dimensional decomposition to ...
متن کامل