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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| 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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| _version_ | 1832548165155291136 |
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| author | Kairen Cai |
| author_facet | Kairen Cai |
| author_sort | Kairen Cai |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fb6e96425c4f4bdc9f94ef743af64d37 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fb6e96425c4f4bdc9f94ef743af64d372025-02-03T06:42:13ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-01241434810.1155/S0161171200003306First eigenvalue of submanifolds in Euclidean spaceKairen Cai0Department of Mathematics, Hangzhou Teachers' College, 96 Wen Yi Road, Hangzhou 310012, ChinaWe 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.http://dx.doi.org/10.1155/S0161171200003306Laplacianeigenvaluesubmanifold. |
| spellingShingle | Kairen Cai First eigenvalue of submanifolds in Euclidean space International Journal of Mathematics and Mathematical Sciences Laplacian eigenvalue submanifold. |
| title | First eigenvalue of submanifolds in Euclidean space |
| title_full | First eigenvalue of submanifolds in Euclidean space |
| title_fullStr | First eigenvalue of submanifolds in Euclidean space |
| title_full_unstemmed | First eigenvalue of submanifolds in Euclidean space |
| title_short | First eigenvalue of submanifolds in Euclidean space |
| title_sort | first eigenvalue of submanifolds in euclidean space |
| topic | Laplacian eigenvalue submanifold. |
| url | http://dx.doi.org/10.1155/S0161171200003306 |
| work_keys_str_mv | AT kairencai firsteigenvalueofsubmanifoldsineuclideanspace |