Upper and lower bounds for Eigenvalues of the Laplacian on a spherical CAP
In the following, we derive upper and lower bounds for eigenvalues of the Laplacian on a domain that is a spherical cap whose angular width 2&0 is less than 7i. While previous work of this nature seems to focus on the principle eigenvalue, our results apply to any eigenvalue when 0 < $0 < nil. In addition, some of our results also apply to spherical caps for which 0 < $0 < n . When our estimates for the principle eigenvalue are compared to the results of [4, 8], we find that our upper and lower bounds are sharper.