$L^2$ Curvature Bounds for Area-Minimizing Currents Mod(2)

Zachary Lihn

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arXiv · 2609.26592

$L^2$ Curvature Bounds for Area-Minimizing Currents Mod(2)

Zachary Lihn

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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}.

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Zachary Lihn. 2026-09-22. $L^2$ Curvature Bounds for Area-Minimizing Currents Mod(2). https://arxiv.org/abs/2609.26592

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