TY - JOUR
T1 - Collapsing of connected sums and the eigenvalues of the Laplacian
AU - Takahashi, Junya
N1 - Publisher Copyright:
© 2002 Elsevier Science B.V.
PY - 2002/1/1
Y1 - 2002/1/1
N2 - We study the behavior of the eigenvalues of the Laplacian acting on functions when one side of a connected sum of two closed Riemannian manifolds collapses to a point. We prove that the eigenvalues converge to those of the limit space, by using the method of Anné and Colbois. From this, we obtain a gluing theorem for the eigenvalues.
AB - We study the behavior of the eigenvalues of the Laplacian acting on functions when one side of a connected sum of two closed Riemannian manifolds collapses to a point. We prove that the eigenvalues converge to those of the limit space, by using the method of Anné and Colbois. From this, we obtain a gluing theorem for the eigenvalues.
KW - Collapsing of Riemannian manifolds
KW - Eigenvalue
KW - Laplacian
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U2 - 10.1016/S0393-0440(01)00033-X
DO - 10.1016/S0393-0440(01)00033-X
M3 - Article
AN - SCOPUS:84991663826
SN - 0393-0440
VL - 40
SP - 201
EP - 208
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
IS - 3-4
ER -