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Existence result for minimal hypersurfaces with a prescribed finite number of planar ends. (English) Zbl 0992.53011
By use of tools from nonlinear analysis some authors produced new minimal surfaces in $$R^3$$ [e.g., N. Kapouleas, J. Differ. Geom. 47, 95-169 (1997; Zbl 0936.53006)]; some authors studied the properties of the moduli space of such surfaces [e.g., J. Perez and A. Ros, Indiana Univ. Math. J. 45, 177-204 (1996; Zbl 0864.53008)]. Parallel to what has been done for minimal surfaces in $$R^3$$, the authors develop a gluing procedure to produce for any $$k\geq 2$$ and any $$n\geq 3$$ complete immersed minimal hypersurfaces of $$R^{n+1}$$ which have $$k$$ planar ends. The surfaces are of the topological type of a sphere with $$k$$ punctures and they all have finite total curvature.

##### MSC:
 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related $$n$$-spaces 53A05 Surfaces in Euclidean and related spaces 47H10 Fixed-point theorems
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