Curvature estimates for minimal annuli and non-compact Douglas-Plateau problem (Q5929594)

The authors firstly give curvature estimates for minimal annuli with convex boundary in parallel planes. Then they study the non-compact Douglas-Plateau problem of annular type for \(n\) boundary curves as follows:NEWLINENEWLINENEWLINELet \(L_i\), \(i=1,2,\dots,n\) be disjoint, embedded proper complete curves, at least one of them is non-compact, find a minimal annulus \(A\) such that \(\partial A=\Cup_{i=1}^n L_i\).NEWLINENEWLINENEWLINEBy using the curvature estimates for minimal annuli, the authors solve some cases of the above non-compact Douglas-Plateau problem. They also obtain various necessary conditions for the existence of minimal surfaces.