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Résumé : Let M n9 n > 1, be a compact «-dimensional manifold without boundary and assume that Fo: M n -> U n+{ smoothly immerses M n as a hypersurface in a Euclidean (n + l)-space R π+1 .We say that MQ = F 0 (Af") is moved along its mean curvature vector if there is a whole family F( , t) of smooth immersions with corresponding hypersurfaces M t = F( , t)(M n ) such that