2021/10/04 by Lima, Vanderson, Menezes, Ana
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2110.01139
We prove that every hyperplane passing through the origin in \rrn+1 divides an embedded compact free boundary minimal hypersurface of the euclidean (n+1)-ball in exactly two connected hypersurfaces. We also show that if a region in the (n+1)-ball has mean convex boundary and contains a nullhomologous (n-1)-dimensional equatorial disk, then this region is a closed halfball. Our first result gives evidence to a conjecture by Fraser and Li in any dimension.