Tuesday Seminar of Analysis

Date, time & place Tuesday 16:50 - 18:20 128Room #128 (Graduate School of Math. Sci. Bldg.) ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi

2019/03/05

16:50-18:20   Room #128 (Graduate School of Math. Sci. Bldg.)
Nicholas Edelen (Massachusetts Institute of Technology)
The structure of minimal surfaces near polyhedral cones (English)
[ Abstract ]
We prove a regularity theorem for minimal varifolds which resemble a cone $C_0$ over an equiangular geodesic net. For varifold classes admitting a no-hole'' condition on the singular set, we additionally establish regularity near the cone $C_0 \times R^m$. Our result implies the following generalization of Taylor's structure theorem for soap bubbles: given an $n$-dimensional soap bubble $M$ in $R^{n+1}$, then away from an $(n-3)$-dimensional set, $M$ is locally $C^{1,\alpha}$ equivalent to $R^n$, a union of three half-$n$-planes meeting at $120$ degrees, or an $(n-2)$-line of tetrahedral junctions. This is joint work with Maria Colombo and Luca Spolaor.