Open Access
2009 Generalization of Hadamardʼs Laplace Eigenvalue Formula to Deforming Manifolds
Pavel Grinfeld
J. Geom. Symmetry Phys. 15: 43-52 (2009). DOI: 10.7546/jgsp-15-2009-43-52


For a Euclidean domain with a moving boundary, Hadamardʼs formula relates the rate of change of the Laplace eigenvalues to the normal velocity of the boundary. We generalize Hadamardʼs formula to deforming Riemannian maniforlds with contour boundary moving in a compatible manner. Our analysis finds direct applications in the dynamics of fluid films. The spectrum of the surface Laplacian describes the frequencies of normal oscillations of the filmʼs surface as well as tangential oscillations in thickness.


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Pavel Grinfeld. "Generalization of Hadamardʼs Laplace Eigenvalue Formula to Deforming Manifolds." J. Geom. Symmetry Phys. 15 43 - 52, 2009.


Published: 2009
First available in Project Euclid: 24 May 2017

zbMATH: 1181.35148
MathSciNet: MR2536501
Digital Object Identifier: 10.7546/jgsp-15-2009-43-52

Rights: Copyright © 2009 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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