Spacelike mean curvature 1 surfaces of genus 1 with two ends in de Sitter 3-space

Details Spacelike mean curvature 1 surfaces of genus 1 with two ends in de Sitter 3-space Spacelike mean curvature 1 surfaces of genus 1 with two ends in de Sitter 3-space

2006-05-19

arxiv.org/abs/math/0605550v1

Mathematics

Differential Geometry

16 pages, 6 figures

Scientific paper

We give a mathematical foundation for, and numerical demonstration of, the existence of mean curvature 1 surfaces of genus 1 with either two elliptic ends or two hyperbolic ends in de Sitter 3-space. An end of a mean curvature 1 surface is an ``elliptic end'' (resp. a ``hyperbolic end'') if the monodromy matrix at the end is diagonalizable with eigenvalues in the unit circle (resp. in the reals). Although the existence of the surfaces is numerical, the types of ends are mathematically determined.

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