An existence result for minimal spheres in manifolds with boundary (Q916171)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: An existence result for minimal spheres in manifolds with boundary |
scientific article; zbMATH DE number 4153513
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An existence result for minimal spheres in manifolds with boundary |
scientific article; zbMATH DE number 4153513 |
Statements
An existence result for minimal spheres in manifolds with boundary (English)
0 references
1990
0 references
In [Ann. Math. (2) 113, 1--24 (1981; Zbl 0462.58014)] \textit{J. Sacks} and \textit{K. Uhlenbeck} have proved the existence of a not homotopically trivial minimal sphere in Riemannian manifolds without boundary, having nontrivial second homotopy group. The author extends this result to a 3-manifold with boundary, obtained by deleting an open connected subset from the interior of a compact Riemannian oriented 3-manifold with smooth boundary and having trivial second homotopy group.
0 references
minimal surface
0 references
pull back
0 references
Hodge *-operator
0 references
winding number
0 references
minimal sphere
0 references
3-manifold with boundary
0 references
trivial second homotopy group
0 references
