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— A disk of class C*'", k > 2, strictiy convex for a fiât Riemannian C*"' metric is C*' '-isometric to a strictiy convex domain of thé euclidian plane (Theorem 1). Thanks to this resuit, thé Weingarten's method becomes global. It yieids an intrinsic geometrical necessary and sufficient condition, thé adjustment, for thé existence of globally smooth of class C*'", k > 3, isometric embeddings (or "realizations") of C' disks strictiy convex for C^' metrics with curvature, either positive when thé target 3-space is Euclidean (Theorem 2), or négative when it is Minkowskian (Theorem 4). Key-Words: Plongement isométrique global, disque strictement convexe, méthode de Weingarten globale, courbure positive ou négative, méthode de continuité. 1980A.M.S. Classification: 53C45, 58G20, 35B65. PREMIÈRE PARTIE PLONGEMENT DANS L'ESPACE EUCLIDIEN

Réalisations globalement régulières de disques strictement convexes dans les espaces d'Euclide et de Minkowski par la méthode de Weingarten