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Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds

Published online by Cambridge University Press:  20 November 2018

S. Minakshisundaram  and
Å. Pleijel
S. Minakshisundaram
Affiliation:
Andhra University, Waltair, South India
Å. Pleijel
Affiliation:
Andhra University, Waltair, South India
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Let V be a connected, compact, differentiable Riemannian manifold. If V is not closed we denote its boundary by S. In terms of local coordinates (xi), i = 1, 2, … Ν, the line-element dr is given by where gik (x1, x2, … xN) are the components of the metric tensor on V We denote by Δ the Beltrami-Laplace-Operator and we consider on V the differential equation (1) Δu + λu = 0.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 1 , Issue 3 , 01 June 1949 , pp. 242 - 256
Copyright
Copyright © Canadian Mathematical Society 1949

References

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