A non-geodesic analogue of Reshetnyak’s majorization theorem

Abstract For any real number ? \kappa and integer n ? 4 n\ge 4 , the Cycl ( ) {{\rm{Cycl}}}_{n}\left(\kappa ) condition introduced by Gromov ( CAT(?)-spaces: construction concentration Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 280 (2001), (Geom. i Topol. 7), 100–140, 299–300) is a necessary for metric space to admit an isometric embedding into mathvariant="normal">CAT {\rm{CAT}}\left(\kappa space. geodesic spaces, satisfying {{\rm{Cycl}}}_{4}\left(\kappa equivalent being . In this article, we prove analogue of Reshetnyak’s majorization theorem (possibly non-geodesic) spaces that satisfy condition. It follows from our result general implies conditions all integers 5 5