Full flexibility of the Monge-Ampère system in codimension d∗ − d + 1

We prove that C1,α solutions to the Monge-Ampère system in dimension d and codimension k= d_*-d+1, where d_* denotes the Janet dimension, are dense in the space of continuous functions, for every Hölder exponent $α<1$. Our result strengthens the statement in [Lewicka 2022], obtained for k = 2d_* and based on ideas from [Källen 1978] in the context of the isometric immersion system. It also generalizes the result of [Inauen-Lewicka 2025], where full flexibility was established in dimension $d=2$ and codimension $k=2$. The same proof scheme further yields local full flexibility of isometric immersions of d-dimensional Riemannian metrics into Euclidean space of dimension d_* + 1, generalizing the result in [Lewicka 2025] proved for $d=k=2$. By using techniques of [Conti-De Lellis-Szekelyhidi], the result can be extended to compact manifolds, in codimension (d+1)d_*-d+1.