A spherical flatness index and a stability inequality for harmonic pseudospheres
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915892477034496 |
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| author | Buffoni, Andrea Cupini, Giovanni Lanconelli, Ermanno |
| author_facet | Buffoni, Andrea Cupini, Giovanni Lanconelli, Ermanno |
| contents | We introduce a new flatness index for the boundary of an open subset $Ω$ of $\mathbb{R}^n$, $n\ge 2$. This index provides a necessary condition for $\partialΩ$ to be a harmonic pseudosphere and sufficient conditions for a harmonic pseudosphere to be a Euclidean sphere. These conditions will follow from a stability inequality formulated in terms of a harmonic invariant, the Kuran gap, recently introduced by the last two authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25231 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A spherical flatness index and a stability inequality for harmonic pseudospheres Buffoni, Andrea Cupini, Giovanni Lanconelli, Ermanno Analysis of PDEs Primary: 35B05, Secondary: 31B05, 35B06 We introduce a new flatness index for the boundary of an open subset $Ω$ of $\mathbb{R}^n$, $n\ge 2$. This index provides a necessary condition for $\partialΩ$ to be a harmonic pseudosphere and sufficient conditions for a harmonic pseudosphere to be a Euclidean sphere. These conditions will follow from a stability inequality formulated in terms of a harmonic invariant, the Kuran gap, recently introduced by the last two authors. |
| title | A spherical flatness index and a stability inequality for harmonic pseudospheres |
| topic | Analysis of PDEs Primary: 35B05, Secondary: 31B05, 35B06 |
| url | https://arxiv.org/abs/2603.25231 |