2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152168We give necessary conditions on complete embedded \cmc surfaces with three or four ends subject to reflection symmetries. The respective submoduli spaces are two-dimensional varieties in the moduli spaces of general \cmc surfaces. We characterize fundamental domains of our \cmc surfaces by associated great circle polygons in the three-sphere.latex2e, AMS-latex, 24 pagesDifferential GeometryModuli Spaces of Embedded Constant Mean Curvature Surfaces with Few Ends and Special Symmetrytext