2006/05/19 by Shoichi Fujimori, Fujimori, Shoichi
Mathematics · #53A10 #53B30 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53A10 #msc:53B30
paper · pdf · doi:10.48550/arxiv.math/0605550
16 pages, 6 figures
arxiv created 2006/05/19 · openalex publication_date 2006/05/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.