$L^p$-Hodge Decomposition with Sobolev classes in Sub-Riemannian Contact Manifolds
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909634368897024 |
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| author | Baldi, Annalisa Rosa, Alessandro |
| author_facet | Baldi, Annalisa Rosa, Alessandro |
| contents | Let $1<p<\infty$. In this article we establish an $L^p$-Hodge decomposition theorem on sub-Riemannian compact contact manifolds without boundary, related to the Rumin complex of differential forms. Given an $L^p$- Rumin's form, we adopt an approach in the spirit of Morrey's book to obtain a decomposition with higher regular ``primitives'' i.e. that belong to suitable Sobolev classes. Our proof relies on recent results obtained in [4] and [6]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16620 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $L^p$-Hodge Decomposition with Sobolev classes in Sub-Riemannian Contact Manifolds Baldi, Annalisa Rosa, Alessandro Analysis of PDEs Differential Geometry 58A10, 35R03, 26D15, 35H10, 53D10, 43A80, 58J99, 46E35 Let $1<p<\infty$. In this article we establish an $L^p$-Hodge decomposition theorem on sub-Riemannian compact contact manifolds without boundary, related to the Rumin complex of differential forms. Given an $L^p$- Rumin's form, we adopt an approach in the spirit of Morrey's book to obtain a decomposition with higher regular ``primitives'' i.e. that belong to suitable Sobolev classes. Our proof relies on recent results obtained in [4] and [6]. |
| title | $L^p$-Hodge Decomposition with Sobolev classes in Sub-Riemannian Contact Manifolds |
| topic | Analysis of PDEs Differential Geometry 58A10, 35R03, 26D15, 35H10, 53D10, 43A80, 58J99, 46E35 |
| url | https://arxiv.org/abs/2502.16620 |