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On minimal submanifolds in an Euclidean space

✍ Scribed by Qiaoling Wang

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
90 KB
Volume
261-262
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The concepts “super stable” and “super index” for minimal submanifolds in a Euclidean space are introduced. These concepts coincide with the usual concepts “stable” and “index” when the submanifolds have codimension one. We prove that the only complete super stable minimal submanifolds of finite total scalar curvature and of dimension not less than three in a Euclidean space are affine planes. We also prove that a complete minimal submanifold of dimension larger or equal to three in a Euclidean space with finite super index has finitely many ends. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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