Constancy of the index for gradient mappings
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918045501358080 |
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| author | Guerra, André Tione, Riccardo |
| author_facet | Guerra, André Tione, Riccardo |
| contents | We show that if the Hessian of a $C^{1,1}$ function has uniformly positive determinant almost everywhere then its index is locally constant, as conjectured by Šverák in 1992. We deduce this result as a consequence of a more general theorem valid for quasiregular gradient mappings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03906 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constancy of the index for gradient mappings Guerra, André Tione, Riccardo Analysis of PDEs Complex Variables Differential Geometry We show that if the Hessian of a $C^{1,1}$ function has uniformly positive determinant almost everywhere then its index is locally constant, as conjectured by Šverák in 1992. We deduce this result as a consequence of a more general theorem valid for quasiregular gradient mappings. |
| title | Constancy of the index for gradient mappings |
| topic | Analysis of PDEs Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2506.03906 |