An existence result for minimal spheres in manifolds with boundary
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.
scientific article; zbMATH DE number 4153513