Existence result for minimal hypersurfaces with a prescribed finite number of planar ends

Saadia Fakhi; Frank Pacard

doi:10.1007/PL00005863

Existence result for minimal hypersurfaces with a prescribed finite number of planar ends

Saadia Fakhi
, Frank Pacard

Université de PARIS XII

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	465-512
Number of pages	48
Journal	Manuscripta Mathematica
Volume	103
Issue number	4
DOIs	https://doi.org/10.1007/PL00005863
Publication status	Published - 1 Jan 2000
Externally published	Yes

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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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AU - Pacard, Frank

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N2 - 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.

AB - 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.

U2 - 10.1007/PL00005863

DO - 10.1007/PL00005863

M3 - Article

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SP - 465

EP - 512

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

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ER -

Existence result for minimal hypersurfaces with a prescribed finite number of planar ends

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