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Compact singular minimal surfaces with boundary. (arXiv:1809.10741v1 [math.DG])
来源于:arXiv
We study of the shape of a compact singular minimal surface in terms of the
geometry of its boundary, asking what type of {\it a priori} information can be
obtained on the surface from the knowledge of its boundary. We derive estimates
of the area and the height in terms of the boundary. In case that the boundary
is a circle, we study under what conditions the surface is rotational. Finally,
we deduce non-existence results when the boundary is formed by two curves that
are sufficiently far apart. 查看全文>>