We show that every oriented area-minimizing cone in “A Sufficient Criterion for a Cone to be Area-Minimizing” [G.R. Lawlor, Mem. of the Amer. Math. Soc., Vol. 91, 1991] can be realized as a tangent cone at a singular point of some homologically area-minimizing singular compact submanifold.
"On realization of tangent cones of homologically area-minimizing compact singular submanifolds." J. Differential Geom. 109 (1) 177 - 188, May 2018. https://doi.org/10.4310/jdg/1525399219