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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.28909 |
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| _version_ | 1866912989844602880 |
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| author | Cao, Wentao Hirsch, Jonas Inauen, Dominik Lewicka, Marta |
| author_facet | Cao, Wentao Hirsch, Jonas Inauen, Dominik Lewicka, Marta |
| contents | We prove that $\mathcal{C}^{1,α}$ 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 $(d+1)d_*-d+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28909 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Full flexibility of the Monge-Ampère system in codimension $d_*-d+1$ Cao, Wentao Hirsch, Jonas Inauen, Dominik Lewicka, Marta Analysis of PDEs We prove that $\mathcal{C}^{1,α}$ 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 $(d+1)d_*-d+1$. |
| title | Full flexibility of the Monge-Ampère system in codimension $d_*-d+1$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.28909 |