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First eigenvalue of submanifolds in Euclidean space

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  • Kairen Cai

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.

Suggested Citation

  • Kairen Cai, 2000. "First eigenvalue of submanifolds in Euclidean space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:934136
    DOI: 10.1155/S0161171200003306
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