2021/04/19 by Choe, Jaigyoung
#49Q05 #53A10 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2104.09087
Given a noncompact disconnected complete periodic curve Γ with no self intersection in \mathbb R3, it is proved that there exists a noncompact simply connected periodic minimal surface spanning Γ. As an application it is shown that for any tetrahedron T with dihedral angles ≤90^∘ there exist four embedded minimal annuli in T which are perpendicular to ∂ T along their boundary. It is also proved that every Platonic solid of \mathbb R3 contains five types of free boundary embedded minimal surfaces of genus zero.