Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2504.03582 |
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Inhaltsangabe:
- We prove that every $\mathcal{C}^1(\barω)$-regular subsolution of the Monge-Ampère system posed on a $2$-dimensional domain $ω$ and with target codimension $2$, can be uniformly approximated by its exact solutions with regularity $\mathcal{C}^{1,α}(\barω)$ for any $α<\min\{1, \frac{s+β}{2}\}$, where $\mathcal{C}^{s,β}$ is the assumed regularity of the system's right hand side. This result suggests the full flexibility of Poznyak's theorem for isometric immersions of $2$d Riemannian manifolds into $\mathbb{R}^4$, and asserts it in the parallel setting of the Monge-Ampère system.