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Journal article
GENERALIZATION OF HADAMARD'S LAPLACE EIGENVALUE FORMULA TO DEFORMING MANIFOLDS
Journal of geometry and symmetry in physics, v 15, pp 43-52
01 Jan 2009
Abstract
For a Euclidean domain with a moving boundary, Hadamard's formula relates the rate of change of the Laplace eigenvalues to the normal velocity of the boundary. We generalize Hadamard's 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 film's surface as well as tangential oscillations in thickness.
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Details
- Title
- GENERALIZATION OF HADAMARD'S LAPLACE EIGENVALUE FORMULA TO DEFORMING MANIFOLDS
- Creators
- Pavel Grinfeld - Drexel University
- Publication Details
- Journal of geometry and symmetry in physics, v 15, pp 43-52
- Publisher
- Inst Biophysics & Biomedical Engineering, Bulgarian Acad Sciences
- Number of pages
- 10
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000436552900002
- Scopus ID
- 2-s2.0-77955038962
- Other Identifier
- 991019312369804721
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- Web of Science research areas
- Physics, Mathematical