A new, self-contained proof of Shahgholian's theorem using the thickness function
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917372127870976 |
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| author | Barkatou, Mohammed |
| author_facet | Barkatou, Mohammed |
| contents | This note presents a new, self-contained proof of Shahgholian's geometric theorem on quadrature surfaces using the thickness function and level set methods. By relying on a radial parametrisation and fundamental maximum principles, the proof avoids the technical complexity of the moving plane method. It provides a more conceptual view, revealing that the overdetermined condition forces all level sets to be parallel to the convex hull of the support of the measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29084 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A new, self-contained proof of Shahgholian's theorem using the thickness function Barkatou, Mohammed Analysis of PDEs 35R35, 35N25, 35B50, 31B20, 35J15 This note presents a new, self-contained proof of Shahgholian's geometric theorem on quadrature surfaces using the thickness function and level set methods. By relying on a radial parametrisation and fundamental maximum principles, the proof avoids the technical complexity of the moving plane method. It provides a more conceptual view, revealing that the overdetermined condition forces all level sets to be parallel to the convex hull of the support of the measure. |
| title | A new, self-contained proof of Shahgholian's theorem using the thickness function |
| topic | Analysis of PDEs 35R35, 35N25, 35B50, 31B20, 35J15 |
| url | https://arxiv.org/abs/2603.29084 |