Abstract:
Paralleling what has been done for minimal surfaces in ℝ3, we develop a gluing procedure to produce, for any k≥ 2 and any n≥ 3 complete immersed minimal hypersurfaces of ℝn +1 which have k planar ends. These surfaces are of the topological type of a sphere with k punctures and they all have finite total curvature.
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Received: 1 July 1999 / Revised version: 31 May 2000
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Fakhi, S., Pacard, F. Existence result for minimal hypersurfaces¶with a prescribed finite number of planar ends. manuscripta math. 103, 465–512 (2000). https://doi.org/10.1007/PL00005863
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DOI: https://doi.org/10.1007/PL00005863