solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看127次
Existence and regularity results for minimal sets; Plateau problem. (arXiv:1807.05663v1 [math.CA])
来源于:arXiv
Solving the Plateau problem means to find the surface with minimal area among
all surfaces with a given boundary. Part of the problem actually consists of
giving a suitable definition to the notions of 'surface', 'area' and
'boundary'. In our setting the considered objects are sets whose Hausdorff area
is locally finite. The sliding boundary condition is given in term of a one
parameter family of compact deformations which allows the boundary of the
surface to moove along a closed set. The area functional is related to
capillarity and free-boundary problems, and is a slight modification of the
Hausdorff area. We focused on minimal boundary cones; that is to say tangent
cones on boundary points of sliding minimal surfaces. In particular we studied
cones contained in an half-space and whose boundary can slide along the
bounding hyperplane. After giving a classification of one-dimensional minimal
cones in the half-plane we provided four new two-dimensional minimal cones in
the three-dimen 查看全文>>