International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 1, Pages 43-48

First eigenvalue of submanifolds in Euclidean space

Kairen Cai

Department of Mathematics, Hangzhou Teachers' College, 96 Wen Yi Road, Hangzhou 310012, China

Received 23 April 1999

Copyright © 2000 Kairen Cai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.