Decoupling for degenerate hypersurfaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909674288185344 |
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| author | Li, Jianhui Yang, Tongou |
| author_facet | Li, Jianhui Yang, Tongou |
| contents | We utilise the two principles of decoupling introduced in arXiv:2407.16108 to prove the following conditional result: assuming uniform decoupling for graphs of polynomials in all dimensions with identically zero Gaussian curvature, we can prove decoupling for all smooth hypersurfaces in all dimensions. Moreover, we are able to prove (unconditional) decoupling for all smooth hypersurfaces in $\mathbb R^4$ and graphs of homogeneous polynomials in $\mathbb R^5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02134 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decoupling for degenerate hypersurfaces Li, Jianhui Yang, Tongou Classical Analysis and ODEs 42B99 We utilise the two principles of decoupling introduced in arXiv:2407.16108 to prove the following conditional result: assuming uniform decoupling for graphs of polynomials in all dimensions with identically zero Gaussian curvature, we can prove decoupling for all smooth hypersurfaces in all dimensions. Moreover, we are able to prove (unconditional) decoupling for all smooth hypersurfaces in $\mathbb R^4$ and graphs of homogeneous polynomials in $\mathbb R^5$. |
| title | Decoupling for degenerate hypersurfaces |
| topic | Classical Analysis and ODEs 42B99 |
| url | https://arxiv.org/abs/2507.02134 |