First eigenvalue of submanifolds in Euclidean space

Kairen Cai

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 24, 1-6

Abstract:

We give some estimates of the first eigenvalue of the Laplacian for compact and non-compact submanifold immersed in the Euclidean space by using the square length of the second fundamental form of the submanifold merely. Then some spherical theorems and a nonimmersibility theorem of Chern and Kuiper type can be obtained.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:934136

DOI: 10.1155/S0161171200003306

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