2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146415We study the rigidity of complete, embedded constant mean curvature surfaces in R^3. Among other things, we prove that when such a surface has finite genus, then intrinsic isometries of the surface extend to isometries of R^3 or its isometry group contains an index two subgroup of isometries that extend.10 pagesDifferential Geometry53A10text