Minimal hypersurfaces asymptotic to Simons cones

Laurent Mazet (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

In this paper, we prove that, up to similarity, there are only two minimal hypersurfaces in $\mathbb{R}^{n+2}$ that are asymptotic to a Simons cone, i.e. the minimal cone over the minimal hypersurface $\sqrt{\frac pn}\mathbb{S}^p\times \sqrt{\frac{n-p}n} \mathbb{S}^{n-p}$ of $\mathbb{S}^{n+1}$

Domaines: Géométrie différentielle [math.DG]

Laurent Mazet. Minimal hypersurfaces asymptotic to Simons cones. Journal of the Institute of Mathematics of Jussieu, 2017, 16 (1), pp.39-58. ⟨10.1017/S1474748015000110⟩. ⟨hal-01023094⟩