The singular set of minimal surfaces near polyhedral cones

Vortrag von Dr. Nicholas Edelen

Sprecher eingeladen von: Prof. Dr. Camillo De Lellis

Datum: 21.12.17  Zeit: 18.10 - 19.30  Raum: Y27H35/36 CANCELLED

We adapt the method of Simon to prove a $C^{1,\alpha}$-regularity theorem for minimal varifolds which resemble a cone $C_0^2$ 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 $C_0^2 \times R^m$. Combined with work of Allard, Simon, Taylor, and Naber-Valtorta, our result implies a $C^{1,\alpha}$-structure for the top three strata of minimizing clusters and size-minimizing currents, and a Lipschitz structure on the $(n-3)$-stratum. This is joint work with Maria Colombo and Luca Spolaor.