Improvement of flatness in annuli
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911672216584192 |
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| author | Fernández-Real, Xavier Florit-Simon, Enric Serra, Joaquim |
| author_facet | Fernández-Real, Xavier Florit-Simon, Enric Serra, Joaquim |
| contents | We present a short and flexible improvement-of-flatness argument adapted to the setting of exterior domains, where one is naturally led to work with annuli instead of balls.
As a model application in the classical setting of minimal surfaces, we give an alternative proof of the end-structure and asymptotics for finite Morse index minimal hypersurfaces with Euclidean area growth in low dimensions.
The method is largely PDE-based and general in its application. Suitable variants have been employed in Bernoulli and Allen--Cahn settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11110 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Improvement of flatness in annuli Fernández-Real, Xavier Florit-Simon, Enric Serra, Joaquim Differential Geometry Analysis of PDEs 35J61, 49Q05 We present a short and flexible improvement-of-flatness argument adapted to the setting of exterior domains, where one is naturally led to work with annuli instead of balls. As a model application in the classical setting of minimal surfaces, we give an alternative proof of the end-structure and asymptotics for finite Morse index minimal hypersurfaces with Euclidean area growth in low dimensions. The method is largely PDE-based and general in its application. Suitable variants have been employed in Bernoulli and Allen--Cahn settings. |
| title | Improvement of flatness in annuli |
| topic | Differential Geometry Analysis of PDEs 35J61, 49Q05 |
| url | https://arxiv.org/abs/2605.11110 |