The singular set of minimal surfaces near polyhedral cones
The singular set of minimal surfaces near polyhedral cones
We adapt the method of Simon [26] to prove a $C^{1,\alpha}$-regularity theorem for minimal varifolds which resemble a cone $\mathbf{C}^2_0$ over an equiangular geodesic net. For varifold classes admitting a "no-hole" condition on the singular set, we additionally establish $C^{1,\alpha}$-regularity near the cone $\mathbf{C}^2_0 \times \mathbb{R}^m$. Combined with work of …