First eigenvalue of submanifolds in Euclidean space
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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200003306 |
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| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |