Year: 2026
Type: preprint
Abstract: We generalize Moser's stability theorem for minimal hypersurface foliations to arbitrary codimension. Let $\mathbb{T}^N=\mathbb{R}^N/\mathbb{Z}^N$ be the standard torus, and let $P\subset\mathbb{R}^N$ be an $m$-plane satisfying a Diophantine condition relative to $\mathbb{Z}^N$. We prove that, under every sufficiently small smooth $\mathbb{Z}^N$-periodic perturbation of the Euclidean metric, the affine foliation of $\mathbb{T}^N$ induced by $P$ persists as a smoothly conjugate foliation by minimal $m$-dimensional submanifolds. The normalized conjugating displacement depends smoothly and tamely on the metric and is locally unique. Moreover, the perturbed foliation admits a common smooth calibration, hence the lifted leaves are area-minimizing. The proof uses Hamilton's formulation of the Nash-Moser implicit function theorem.
Source: arXiv (Cornell University)
Author: Nguyen, Hoan
Institution: University of Chicago
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221762068