Abstract

Abstract:

We obtain compact orientable embedded surfaces with constant mean curvature $0<H<\{1\\over 2\}$ and arbitrary genus in $\Bbb\{S\}^2\times\\Bbb\{R\}$. These surfaces have dihedral symmetry and desingularize a pair of spheres with mean curvature $\{1\over 2\}$ tangent along an equator. This is a particular case of a conjugate Plateau construction of doubly periodic surfaces with constant mean curvature in $\Bbb\{S\}^2\times\Bbb\{R\}$, $\Bbb\{H\}^2\times\\Bbb\{R\}$, and $\Bbb\{R\}^3$ with bounded height and enjoying the symmetries of certain tessellations of $\Bbb\{S\}^2$, $\Bbb\{H\}^2$, and $\Bbb\{R\}^2$ by regular polygons.

pdf

Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1981-1994
Launched on MUSE
2020-11-11
Open Access
No
Back To Top

This website uses cookies to ensure you get the best experience on our website. Without cookies your experience may not be seamless.