Corpus ID: 203610459

Regularity of minimal surfaces near quadratic cones

  title={Regularity of minimal surfaces near quadratic cones},
  author={Nick Edelen and Luca Spolaor},
  journal={arXiv: Differential Geometry},
Hardt-Simon proved that every area-minimizing hypercone $\mathbf{C}$ having only an isolated singularity fits into a foliation of $\mathbb{R}^{n+1}$ by smooth, area-minimizing hypersurfaces asymptotic to $\mathbf{C}$. In this paper we prove that if a stationary $n$-varifold $M$ in the unit ball $B_1 \subset \mathbb{R}^{n+1}$ lies sufficiently close to a minimizing quadratic cone (for example, the Simons' cone $\mathbf{C}^{3,3}$), then $\mathrm{spt} M \cap B_{1/2}$ is a $C^{1,\alpha… Expand
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