Author

Zachary Lihn

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Preprint Sep 2026

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

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 modul...

Zachary Lihn · 0 citations

Preprint Sep 2026

Stationary varifolds with singularities II

For every dimension $m\geq 3$, we show the existence of an open set $U\subset \mathbb R^{m+1}$, a smooth Riemannian metric $g$ on it, and an integral $m$-dimensional stationary varifold $V$ in $(U,g)$ with the following properties. $V$ has a flat tangent plane of multiplicity $2$ at an interior point $p$, it is a smoot...

Camillo De Lellis, Jonas Hirsch, Zachary Lihn et al. · 0 citations