Improvement of flatness in annuli
Differential Geometry
2026-05-13 v1 Analysis of PDEs
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.
Cite
@article{arxiv.2605.11110,
title = {Improvement of flatness in annuli},
author = {Xavier Fernández-Real and Enric Florit-Simon and Joaquim Serra},
journal= {arXiv preprint arXiv:2605.11110},
year = {2026}
}