Regularity of Area-Minimizing Surfaces
The proof of the regularity of an area-minimizing surface with a given smooth boundary has had a long and interesting history. Following work of Douglas, Rado, and Osserman, Gulliver [1973, G] proved that a least-area map of a disc into R3 with prescribed boundary is a smooth immersion on the interior. The map need not be an embedding and cannot be if the boundary curve is knotted. The possibility of boundary branch points remains open today. Continue reading ‘Regularity of Area-Minimizing Surfaces’ »
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