Uniform Sobolev, interpolation and geometric Calderón-Zygmund inequalities for graph hypersurfaces
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929383335264256 |
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| author | Della Corte, Serena Diana, Antonia Mantegazza, Carlo |
| author_facet | Della Corte, Serena Diana, Antonia Mantegazza, Carlo |
| contents | In this note, our aim is to show that families of smooth hypersurfaces of $\mathbb R^{n+1}$ which are all $C^1$--close enough to a fixed compact, embedded one, have uniformly bounded constants in some relevant inequalities for mathematical analysis, like Sobolev, Gagliardo-Nirenberg and ``geometric'' Calderón-Zygmund inequalities. This technical result is quite useful, in particular, in the study of the geometric flows of hypersurfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_04013 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform Sobolev, interpolation and geometric Calderón-Zygmund inequalities for graph hypersurfaces Della Corte, Serena Diana, Antonia Mantegazza, Carlo Differential Geometry 53C42 35A23 47J20 In this note, our aim is to show that families of smooth hypersurfaces of $\mathbb R^{n+1}$ which are all $C^1$--close enough to a fixed compact, embedded one, have uniformly bounded constants in some relevant inequalities for mathematical analysis, like Sobolev, Gagliardo-Nirenberg and ``geometric'' Calderón-Zygmund inequalities. This technical result is quite useful, in particular, in the study of the geometric flows of hypersurfaces. |
| title | Uniform Sobolev, interpolation and geometric Calderón-Zygmund inequalities for graph hypersurfaces |
| topic | Differential Geometry 53C42 35A23 47J20 |
| url | https://arxiv.org/abs/2304.04013 |