Embedded minimal disks with a free boundary on a polyhedron in \({\mathbb R}^ 3\) (Q1096187)
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scientific article; zbMATH DE number 4030384
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Embedded minimal disks with a free boundary on a polyhedron in \({\mathbb R}^ 3\) |
scientific article; zbMATH DE number 4030384 |
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Embedded minimal disks with a free boundary on a polyhedron in \({\mathbb R}^ 3\) (English)
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1988
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We show that a convex polyhedron in Euclidean 3-space bounds an embedded minimal surface meeting this polyhedron orthogonally along its boundary. The minimal surface is nontrivial in the sense that it does not coincide with a face and does not contain an edge of the polyhedron in its boundary. The proof is based on previous results of the author for smooth free boundaries, a blow-up argument, and barrier constructions utilizing catenoids.
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minimal surface
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smooth free boundaries
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catenoids
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boundary on a polyhedron
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