This analysis demonstrates uniform approximation of solutions in 2D Riemannian manifolds, suggesting broader implications for geometrical theory.
We prove that every C¹(ω)-regular subsolution of the Monge-Amp\`ere system posed on a $2$-dimensional domain ω and with target codimension $2$, can be uniformly approximated by its exact solutions with regularity C1,α(ω) for any α<1. This result asserts flexibility of Poznyak's theorem for isometric immersions of $2$d Riemannian manifolds into R⁴, in the parallel setting of the Monge-Amp\`ere system.
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Inauen et al. (2025) studied this question.
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