Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms

Abstract

We present a theorem on the unitarizability of loop group valued monodromy representations and apply this to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the simply-connected 3-dimensional space forms ${\mathbb{R}}^3$, $\bbS^3 $ and $\bbH^3$. Additionally, we compute the extended frame for any associated family of Delaunay surfaces.

18 pages, revised version

References in corpus (1)

• Coplanar constant mean curvature surfaces

Cited by in corpus (21)

• Holomorphic Representation of Constant Mean Curvature Surfaces in Minkowski Space: Consequences of Non-Compactness in Loop Group Methods
• Equivariant harmonic cylinders
• Deformations of symmetric CMC surfaces in the 3-sphere
• On the moduli of constant mean curvature cylinders of finite type in the 3-sphere
• Minimal n-Noids in hyperbolic and anti-de Sitter 3-space
• Constant mean curvature surfaces based on fundamental quadrilaterals
• Constant Mean Curvature n-noids with Platonic Symmetries
• Discrete constant mean curvature surfaces via conserved quantities
• Constant mean curvature surfaces in hyperbolic 3-space via loop groups
• Lawson's genus two minimal surface and meromorphic connections
• On infinitesimal deformations of cmc surfaces of finite type in the 3-sphere
• Gluing Delaunay ends to minimal n-noids using the DPW method
• Simultaneous unitarizability of SL_n(C)-valued maps, and constant mean curvature k-noid monodromy
• DPW Potentials for Compact Symmetric CMC Surfaces in ${\mathbb{S}}^3$
• Constant Mean Curvature Trinoids with one Irregular End
• Constant mean curvature n-noids in hyperbolic space
• Complete families of embedded high genus CMC surfaces in the 3-sphere (with an appendix by Steven Charlton)
• Area Estimates for High genus Lawson surfaces via DPW
• Corresponding constant mean curvature surfaces in hyperbolic and Euclidean 3-spaces
• Constant mean curvature cylinders with irregular ends
• Minimal Lagrangian surfaces in the two dimensional complex quadric via the loop group method