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arXiv · 2605.11110

Improvement of flatness in annuli

Xavier Fernández-Real·Enric Florit-Simon·Joaquim Serra
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Abstract

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.

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Xavier Fernández-Real, Enric Florit-Simon, Joaquim Serra. 2026-05-11. Improvement of flatness in annuli. https://arxiv.org/abs/2605.11110

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