We adapt the method of Simon [26] to prove a $C^{1,\alpha}$-regularity theorem for minimal varifolds which resemble cone $\mathbf{C}^2_0$ over an equiangular geodesic net. For varifold classes admitting “no-hole” condition on singular set, we additionally establish near $\mathbf{C}^2_0 \times \mathbb{R}^m$. Combined with work Allard [2], [26], Taylor [29], and Naber–Valtorta [21], our result im...

Let X be a finite-dimensional normed space and let Y⊆X its proper linear subspace. The set of all minimal projections from to Y is convex subset the operators we can consider affine dimension. We establish several results on possible values this prove optimal upper bounds in terms dimensions Y. Moreover, improve these estimates polyhedral spaces for an open dense subspaces given As consequence,...