Year: 2026
Type: preprint
Abstract: We prove \emph{a priori} interior $L^2$ bounds for the second fundamental form of area-minimizing currents modulo $2$ in every dimension $n\geq 2$ and arbitrary codimension. The bounds depend only on the dimension, codimension, and an upper bound for the mass. As a corollary, we show that area-minimizing surfaces modulo $2$ with bounded area lie in finitely many diffeomorphism classes. This answers a question of \cite{Liu2020WeakCounterexamples}.
Source: arXiv (Cornell University)
Author: Lihn, Zachary
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7214120648