2021/09/27 by Barbosa, Ezequiel, de Carvalho, Alcides, Santos, Roney
#53A10 #58J32 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2109.13007
In this work, we prove that any two free boundary minimal hypersurfaces in the unit Euclidean ball have an intersection point in any half-ball. This is a strong version of the Frankel property proved by A. Fraser and M. Li \citeFRLI. As a consequence, we obtain the two-piece property for free boundary minimal hypersurfaces in the unit ball: every equatorial disk divides any compact minimal hypersurface with free boundary in the unit ball in two connected pieces.