Uniqueness of Cylindrical Tangent Cones $C_{p,q}\times \mathbb{R}$

Abstract

We show the uniqueness of the cylindrical tangent cone $C({\mathbb{S}}^2\times {\mathbb{S}}^4)\times \mathbb{R}$ for area-minimizing hypersurfaces in ${\mathbb{R}}^9$, completing the uniqueness of all tangent cones of the form $C_{p,q}\times \mathbb{R}$ proved by Simon for dimensions at least 10 and Székelyhidi for the Simons cone.

10 pages