Year: 2026
Type: article
Abstract: We construct area-minimizing submanifolds with fractal singular sets on compact Riemannian manifolds. Thus, we settle a conjecture of Almgren, and our answer is sharp dimension-wise. Furthermore, we can prescribe arbitrarily the strata in the Almgren stratification of the singular sets of our area-minimizing submanifolds, and our results hold in the category of integral currents, mod v currents and stable stationary varifolds.
Source: Annals of Mathematics
Author: Zhenhua Liu
Institution: Princeton University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4286895426