EIGENVALUES OF THE LAPLACIAN ON A GEODESIC BALL IN THE n-SPHERE

Let λ(n, r) and μ(n,r) be the first Dirichlet eigenvalue and the lowest nonzero Neumann eigenvalue of a geodesic ball B(r), of radius r, in the unit n-sphere sn or the real projective space pn, respectively. In this paper we compute the radii or B(r) such that λ(n, r) or, respectively, μ(n,r) is equ...

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Bibliographic Details
Published in:Chinese journal of mathematics (Taipei, Taiwan) Taiwan), 1987-12, Vol.15 (4), p.237-245
Main Author: BANG, SEUNG-JIN
Format: Article
Language:English
Subjects:
Boundary conditions
Eigenfunctions
Eigenvalues
Hemispheres
Hypergeometric functions
Integers
Laplacians
Mathematical functions
Polynomials
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Summary:Let λ(n, r) and μ(n,r) be the first Dirichlet eigenvalue and the lowest nonzero Neumann eigenvalue of a geodesic ball B(r), of radius r, in the unit n-sphere sn or the real projective space pn, respectively. In this paper we compute the radii or B(r) such that λ(n, r) or, respectively, μ(n,r) is equal to k(n+k-1) (k = 1,2,3, ...) or k(k-1)-n(n-2)/4(2k > n). Moreover, we find the procedure which estimates the small Dirichlet eigenvalues of B(r). Some conjectures will be presented.
ISSN:0379-7570