Some existence results about radial graphs of constant mean curvature with boundary in parallel planes (Q960016)

This article presents new results regarding the existence of radial constant mean curvature H annulus spanning two given Jordan curves in parallel planes of Euclidean 3-space. This work represents the continuation of some previous papers by the same authors. The novel aspects compared to both previous papers, are that the curves do not have to be convex and at the same time the orthogonal projection of the curve \(c_1\) on the plane of the curve \(c_2\) is not required to lie in the interior of the region bounded by \(c_2\). Based on specific considerations regarding the geometry of the curves, the authors prove the existence of a constant mean curvature (H positive) surface whose boundary represents the union of the two curves, and which is topologically an annulus.